Log in

Relevant bibliographies by topics / Discrete Mathematics and Combinatorics / Dissertations / Theses

To see the other types of publications on this topic, follow the link: Discrete Mathematics and Combinatorics.

Dissertations / Theses on the topic 'Discrete Mathematics and Combinatorics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 dissertations / theses for your research on the topic 'Discrete Mathematics and Combinatorics.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.

1

Samieinia, Shiva. "Digital Geometry, Combinatorics, and Discrete Optimization." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-47399.

Full text

Abstract:

This thesis consists of two parts: digital geometry and discrete optimization. In the first part we study the structure of digital straight line segments. We also study digital curves from a combinatorial point of view. In Paper I we study the straightness in the 8-connected plane and in the Khalimsky plane by considering vertical distances and unions of two segments. We show that we can investigate the straightness of Khalimsky arcs by using our knowledge from the 8-connected plane. In Paper II we determine the number of Khalimsky-continuous functions with 2, 3 and 4 points in their codomain.

APA, Harvard, Vancouver, ISO, and other styles

2

Dobbins, Michael Gene. "Representations of Polytopes." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/141523.

Full text

Abstract:

Mathematics<br>Ph.D.<br>Here we investigate a variety of ways to represent polytopes and related objects. We define a class of posets, which includes all abstract polytopes, giving a unique representative among posets having a particular labeled flag graph and characterize the labeled flag graphs of abstract polytopes. We show that determining the realizability of an abstract polytope is equivalent to solving a low rank matrix completion problem. For any given polytope, we provide a new construction for the known result that there is a combinatorial polytope with a specified ridge that is alwa

APA, Harvard, Vancouver, ISO, and other styles

3

Bennett, Robert. "Fibonomial Tilings and Other Up-Down Tilings." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/84.

Full text

Abstract:

The Fibonomial coefficients are a generalization of the binomial coefficients with a rather nice combinatorial interpretation. While the ordinary binomial coefficients count lattice paths in a grid, the Fibonomial coefficients count the number of ways to draw a lattice path in a grid and then Fibonacci-tile the regions above and below the path in a particular way. We may forgo a literal tiling interpretation and, instead of the Fibonacci numbers, use an arbitrary function to count the number of ways to "tile" the regions of the grid delineated by the lattice path. When the function is a combin

APA, Harvard, Vancouver, ISO, and other styles

4

Falgas-Ravry, Victor. "Thresholds in probabilistic and extremal combinatorics." Thesis, Queen Mary, University of London, 2012. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8827.

Full text

Abstract:

This thesis lies in the field of probabilistic and extremal combinatorics: we study discrete structures, with a focus on thresholds, when the behaviour of a structure changes from one mode into another. From a probabilistic perspective, we consider models for a random structure depending on some parameter. The questions we study are then: When (i.e. for what values of the parameter) does the probability of a given property go from being almost 0 to being almost 1? How do the models behave as this transition occurs? From an extremal perspective, we study classes of structures depending on some

APA, Harvard, Vancouver, ISO, and other styles

5

Barnard, Kristen M. "Some Take-Away Games on Discrete Structures." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/44.

Full text

Abstract:

The game of Subset Take-Away is an impartial combinatorial game posed by David Gale in 1974. The game can be played on various discrete structures, including but not limited to graphs, hypergraphs, polygonal complexes, and partially ordered sets. While a universal winning strategy has yet to be found, results have been found in certain cases. In 2003 R. Riehemann focused on Subset Take-Away on bipartite graphs and produced a complete game analysis by studying nim-values. In this work, we extend the notion of Take-Away on a bipartite graph to Take-Away on particular hypergraphs, namely oddly-un

APA, Harvard, Vancouver, ISO, and other styles

6

Zhoroev, Tilekbek. "Controllability and Observability of Linear Nabla Discrete Fractional Systems." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3156.

Full text

Abstract:

The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of

APA, Harvard, Vancouver, ISO, and other styles

7

Chandrasekhar, Karthik. "BOUNDING THE NUMBER OF COMPATIBLE SIMPLICES IN HIGHER DIMENSIONAL TOURNAMENTS." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/63.

Full text

Abstract:

A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the (n − 1)-dimensional simplex on V is given an orientation. In this dissertation we bound the number of compatible k-simplices, that is we bound the number of k-simplices such that its (k − 1)-faces with the already-specified orientatio

APA, Harvard, Vancouver, ISO, and other styles

8

Aftene, Florin. "Vertex-Relaxed Graceful Labelings of Graphs and Congruences." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2664.

Full text

Abstract:

A labeling of a graph is an assignment of a natural number to each vertex of a graph. Graceful labelings are very important types of labelings. The study of graceful labelings is very difficult and little has been shown about such labelings. Vertex-relaxed graceful labelings of graphs are a class of labelings that include graceful labelings, and their study gives an approach to the study of graceful labelings. In this thesis we generalize the congruence approach of Rosa to obtain new criteria for vertex-relaxed graceful labelings of graphs. To do this, we generalize Faulhaber’s Formula, which

APA, Harvard, Vancouver, ISO, and other styles

9

Uyanik, Meltem. "Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models." TopSCHOLAR®, 2015. http://digitalcommons.wku.edu/theses/1491.

Full text

Abstract:

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main result

APA, Harvard, Vancouver, ISO, and other styles

10

Shi, Tongjia. "Cycle lengths of θ-biased random permutations". Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/65.

Full text

Abstract:

Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or negatively correlated, depending on θ. The mth moment

APA, Harvard, Vancouver, ISO, and other styles

11

Gaslowitz, Joshua Z. "Chip Firing Games and Riemann-Roch Properties for Directed Graphs." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/42.

Full text

Abstract:

The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained.

APA, Harvard, Vancouver, ISO, and other styles

12

Arslan, Aykut. "Discrete Fractional Hermite-Hadamard Inequality." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1940.

Full text

Abstract:

This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard ine

APA, Harvard, Vancouver, ISO, and other styles

13

Hearon, Sean M. "PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/427.

Full text

Abstract:

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.

APA, Harvard, Vancouver, ISO, and other styles

14

Cassels, Joshua, and Anant Godbole. "Covering Arrays for Equivalence Classes of Words." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/honors/446.

Full text

Abstract:

Covering arrays for words of length t over a d letter alphabet are k × n arrays with entries from the alphabet so that for each choice of t columns, each of the dt t-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case, words are equivalent if they induce the same partition of a t element set. In the second case, words of the same weighted sum are equivalent. In both cases we produce logarithmic upper bounds on the minimum size k = k(n) of a covering array. Most definitive result

APA, Harvard, Vancouver, ISO, and other styles

15

Alexander, Matthew R. "Combinatorial and Discrete Problems in Convex Geometry." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1508949236617778.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Xin, Yuxin. "Strongly Eutactic Lattices From Vertex Transitive Graphs." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2171.

Full text

Abstract:

In this thesis, we provide an algorithm for constructing strongly eutactic lattices from vertex transitive graphs. We show that such construction produces infinitely many strongly eutactic lattices in arbitrarily large dimensions. We demonstrate our algorithm on the example of the famous Petersen graph using Maple computer algebra system. We also discuss some additional examples of strongly eutactic lattices obtained from notable vertex transitive graphs. Further, we study the properties of the lattices generated by product graphs, complement graphs, and line graphs of vertex transitive graphs

APA, Harvard, Vancouver, ISO, and other styles

17

Tierney, Patrick N. "Realizing the 2-Associahedron." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/77.

Full text

Abstract:

The associahedron has appeared in numerous contexts throughout the field of mathematics. By representing the associahedron as a poset of tubings, Michael Carr and Satyan L. Devadoss were able to create a gener- alized version of the associahedron in the graph-associahedron. We seek to create an alternative generalization of the associahedron by considering a particle-collision model. By extending this model to what we dub the 2- associahedron, we seek to further understand the space of generalizations of the associahedron.

APA, Harvard, Vancouver, ISO, and other styles

18

James, Lacey Taylor. "Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle." CSUSB ScholarWorks, 2019. https://scholarworks.lib.csusb.edu/etd/835.

Full text

Abstract:

This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can

APA, Harvard, Vancouver, ISO, and other styles

19

Riggle, Matthew. "Runs of Identical Outcomes in a Sequence of Bernoulli Trials." TopSCHOLAR®, 2018. https://digitalcommons.wku.edu/theses/2451.

Full text

Abstract:

The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n consecutive successes (where the nth success occurs on trial XTn ). Likewise, we define T

APA, Harvard, Vancouver, ISO, and other styles

20

Justus, Amanda N. "Permutation Groups and Puzzle Tile Configurations of Instant Insanity II." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2337.

Full text

Abstract:

The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or a 5 x 4 puzzle, respectively. We consider the possibilities when we delete a color

APA, Harvard, Vancouver, ISO, and other styles

21

Er, Aynur. "Stability of Linear Difference Systems in Discrete and Fractional Calculus." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1946.

Full text

Abstract:

The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some m

APA, Harvard, Vancouver, ISO, and other styles

22

Taylor, Clifford T. "Deletion-Induced Triangulations." UKnowledge, 2015. http://uknowledge.uky.edu/math_etds/24.

Full text

Abstract:

Let d > 0 be a fixed integer and let A ⊆ ℝd be a collection of n ≥ d + 2 points which we lift into ℝd+1. Further let k be an integer satisfying 0 ≤ k ≤ n-(d+2) and assign to each k-subset of the points of A a (regular) triangulation obtained by deleting the specified k-subset and projecting down the lower hull of the convex hull of the resulting lifting. Next, for each triangulation we form the characteristic vector defined by Gelfand, Kapranov, and Zelevinsky by assigning to each vertex the sum of the volumes of all adjacent simplices. We then form a vector for the lifting, which we call the

APA, Harvard, Vancouver, ISO, and other styles

23

Lam, Matthew. "A Combinatorial Exploration of Elliptic Curves." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/hmc_theses/91.

Full text

Abstract:

At the intersection of algebraic geometry, number theory, and combinatorics, an interesting problem is counting points on an algebraic curve over a finite field. When specialized to the case of elliptic curves, this question leads to a surprising connection with a particular family of graphs. In this document, we present some of the underlying theory and then summarize recent results concerning the aforementioned relationship between elliptic curves and graphs. A few results are additionally further elucidated by theory that was omitted in their original presentation.

APA, Harvard, Vancouver, ISO, and other styles

24

Miller, Sam. "Combinatorial Polynomial Hirsch Conjecture." Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/109.

Full text

Abstract:

The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the

APA, Harvard, Vancouver, ISO, and other styles

25

Rosenbaum, Leah F. "Exploring the On-line Partitioning of Posets Problem." Scholarship @ Claremont, 2012. http://scholarship.claremont.edu/scripps_theses/53.

Full text

Abstract:

One question relating to partially ordered sets (posets) is that of partitioning or dividing the poset's elements into the fewest number of chains that span the poset. In 1950, Dilworth established that the width of the poset - the size of the largest set composed only of incomparable elements - is the minimum number of chains needed to partition that poset. Such a bound in on-line partitioning has been harder to establish, and work has evalutated classes of posets based on their width. This paper reviews the theorems that established val(2)=5 and illustrates them with examples. It also covers

APA, Harvard, Vancouver, ISO, and other styles

26

Serrato, Alexa. "Reed's Conjecture and Cycle-Power Graphs." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/59.

Full text

Abstract:

Reed's conjecture is a proposed upper bound for the chromatic number of a graph. Reed's conjecture has already been proven for several families of graphs. In this paper, I show how one of those families of graphs can be extended to include additional graphs and also show that Reed's conjecture holds for a family of graphs known as cycle-power graphs, and also for their complements.

APA, Harvard, Vancouver, ISO, and other styles

27

Murphy, Kyle. "On t-Restricted Optimal Rubbling of Graphs." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3251.

Full text

Abstract:

For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertices that are adjacent to v and places one pebble on v. A vertex x is reachable under a pebbling distribution f if there exists some sequence of rubbling and pebbling moves that places a pebble on x. A pebbling distribution where every vertex is reachable is called a rubbling configuration. The t-rest

APA, Harvard, Vancouver, ISO, and other styles

28

Fournier, Bradford M. "Towards a Theory of Recursive Function Complexity: Sigma Matrices and Inverse Complexity Measures." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2072.

Full text

Abstract:

This paper develops a data structure based on preimage sets of functions on a finite set. This structure, called the sigma matrix, is shown to be particularly well-suited for exploring the structural characteristics of recursive functions relevant to investigations of complexity. The matrix is easy to compute by hand, defined for any finite function, reflects intrinsic properties of its generating function, and the map taking functions to sigma matrices admits a simple polynomial-time algorithm . Finally, we develop a flexible measure of preimage complexity using the aforementioned matrix. Thi

APA, Harvard, Vancouver, ISO, and other styles

29

Tung, Jen-Fu. "An Algorithm to Generate Two-Dimensional Drawings of Conway Algebraic Knots." TopSCHOLAR®, 2010. http://digitalcommons.wku.edu/theses/163.

Full text

Abstract:

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of c

APA, Harvard, Vancouver, ISO, and other styles

30

Jung, JiYoon. "ANALYTIC AND TOPOLOGICAL COMBINATORICS OF PARTITION POSETS AND PERMUTATIONS." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/6.

Full text

Abstract:

In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent avo

APA, Harvard, Vancouver, ISO, and other styles

31

Leader, Imre Bennett. "Discrete isoperimetric inequalities and other combinatorial results." Thesis, University of Cambridge, 1989. https://www.repository.cam.ac.uk/handle/1810/250940.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Scott, Hamilton. "Zero Sets in Graphs." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1705.

Full text

Abstract:

Let S ⊆ V be an arbitrary subset of vertices of a graph G = (V,E). The differential ∂(S) equals the difference between the cardinality of the set of vertices not in S but adjacent to vertices in S, and the cardinality of the set S. The differential of a graph G equals the maximum differential of any subset S of V . A set S is called a zero set if ∂(S) = 0. In this thesis we introduce the study of zero sets in graphs. We give proofs of the existence of zero sets in various kinds of graphs such as even order graphs, bipartite graphs, and graphs of maximum degree 3. We also give proofs regarding

APA, Harvard, Vancouver, ISO, and other styles

33

Walvoort, Clayton A. "Peg Solitaire on Trees with Diameter Four." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1113.

Full text

Abstract:

In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for all trees with diameter four. We also give the maximum number of pegs that can be left on such a graph under the restriction that we jump whenever possible.

APA, Harvard, Vancouver, ISO, and other styles

34

Carney, Nicholas. "Roman Domination Cover Rubbling." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3617.

Full text

Abstract:

In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for p

APA, Harvard, Vancouver, ISO, and other styles

35

Ahlbach, Connor Thomas. "A Discrete Approach to the Poincare-Miranda Theorem." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/47.

Full text

Abstract:

The Poincare-Miranda Theorem is a topological result about the existence of a zero of a function under particular boundary conditions. In this thesis, we explore proofs of the Poincare-Miranda Theorem that are discrete in nature - that is, they prove a continuous result using an intermediate lemma about discrete objects. We explain a proof by Tkacz and Turzanski that proves the Poincare-Miranda theorem via the Steinhaus Chessboard Theorem, involving colorings of partitions of n-dimensional cubes. Then, we develop a new proof of the Poincare-Miranda Theorem that relies on a polytopal generaliza

APA, Harvard, Vancouver, ISO, and other styles

36

Clark, Eric Logan. "COMBINATORIAL ASPECTS OF EXCEDANCES AND THE FROBENIUS COMPLEX." UKnowledge, 2011. http://uknowledge.uky.edu/gradschool_diss/158.

Full text

Abstract:

In this dissertation we study the excedance permutation statistic. We start by extending the classical excedance statistic of the symmetric group to the affine symmetric group eSn and determine the generating function of its distribution. The proof involves enumerating lattice points in a skew version of the root polytope of type A. Next we study the excedance set statistic on the symmetric group by defining a related algebra which we call the excedance algebra. A combinatorial interpretation of expansions from this algebra is provided. The second half of this dissertation deals with the topol

APA, Harvard, Vancouver, ISO, and other styles

37

Hlavacek, Magda L. "Random Tropical Curves." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/95.

Full text

Abstract:

In the setting of tropical mathematics, geometric objects are rich with inherent combinatorial structure. For example, each polynomial $p(x,y)$ in the tropical setting corresponds to a tropical curve; these tropical curves correspond to unbounded graphs embedded in $\R^2$. Each of these graphs is dual to a particular subdivision of its Newton polytope; we classify tropical curves by combinatorial type based on these corresponding subdivisions. In this thesis, we aim to gain an understanding of the likeliness of the combinatorial type of a randomly chosen tropical curve by using methods from po

APA, Harvard, Vancouver, ISO, and other styles

38

Eroglu, Cihan. "Omnisculptures." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1346.

Full text

Abstract:

In this thesis we will study conditions for the existence of minimal sized omnipatterns in higher dimensions. We will introduce recent work conducted on one dimensional and two dimensional patterns known as omnisequences and omnimosaics, respectively. These have been studied by Abraham et al [3] and Banks et al [2]. The three dimensional patterns we study are called omnisculptures, and will be the focus of this thesis. A (K,a) omnisequence of length n is a string of letters that contains each of the ak words of length k over [A]={1,2,...a} as a substring. An omnimosaic O(n,k,a) is an n × n mat

APA, Harvard, Vancouver, ISO, and other styles

39

Sengul, Sevgi. "Discrete Fractional Calculus and Its Applications to Tumor Growth." TopSCHOLAR®, 2010. http://digitalcommons.wku.edu/theses/161.

Full text

Abstract:

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractio

APA, Harvard, Vancouver, ISO, and other styles

40

Lin, Matthew. "Graph Cohomology." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/82.

Full text

Abstract:

What is the cohomology of a graph? Cohomology is a topological invariant and encodes such information as genus and euler characteristic. Graphs are combinatorial objects which may not a priori admit a natural and isomorphism invariant cohomology ring. In this project, given any finite graph G, we constructively define a cohomology ring H*(G) of G. Our method uses graph associahedra and toric varieties. Given a graph, there is a canonically associated convex polytope, called the graph associahedron, constructed from G. In turn, a convex polytope uniquely determines a toric variety. We synthesiz

APA, Harvard, Vancouver, ISO, and other styles

41

Moore, Christian G. "Global Supply Sets in Graphs." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3025.

Full text

Abstract:

For a graph G=(V,E), a set S⊆V is a global supply set if every vertex v∈V\S has at least one neighbor, say u, in S such that u has at least as many neighbors in S as v has in V \S. The global supply number is the minimum cardinality of a global supply set, denoted γgs (G). We introduce global supply sets and determine the global supply number for selected families of graphs. Also, we give bounds on the global supply number for general graphs, trees, and grid graphs.

APA, Harvard, Vancouver, ISO, and other styles

42

Creswell, Stephanie A. "The Linear Cutwidth and Cyclic Cutwidth of Complete n-Partite Graphs." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/34.

Full text

Abstract:

The cutwidth of different graphs is a topic that has been extensively studied. The basis of this paper is the cutwidth of complete n-partite graphs. While looking at the cutwidth of complete n-partite graphs, we strictly consider the linear embedding and cyclic embedding. The relationship between the linear cutwidth and the cyclic cutwidth is discussed and used throughout multiple proofs of different cases for the cyclic cutwidth. All the known cases for the linear and cyclic cutwidth of complete bipartite, complete tripartite, and complete n-partite graphs are highlighted. The main focus of t

APA, Harvard, Vancouver, ISO, and other styles

43

Molder, Nathan. "Taking Notes: Generating Twelve-Tone Music with Mathematics." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3592.

Full text

Abstract:

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of diﬀerent musical notes, each of which has diﬀerent sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

APA, Harvard, Vancouver, ISO, and other styles

44

Ball, Cory BH. "The Apprentices' Tower of Hanoi." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2512.

Full text

Abstract:

The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.

APA, Harvard, Vancouver, ISO, and other styles

45

Harris, Elizabeth Marie. "Global Domination Stable Graphs." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1476.

Full text

Abstract:

A set of vertices S in a graph G is a global dominating set (GDS) of G if S is a dominating set for both G and its complement G. The minimum cardinality of a global dominating set of G is the global domination number of G. We explore the effects of graph modifications on the global domination number. In particular, we explore edge removal, edge addition, and vertex removal.

APA, Harvard, Vancouver, ISO, and other styles

46

Liendo, Martha Louise. "Preferential Arrangement Containment in Strict Superpatterns." Digital Commons @ East Tennessee State University, 2012. https://dc.etsu.edu/etd/1428.

Full text

Abstract:

Most results on pattern containment deal more directly with pattern avoidance, or the enumeration and characterization of strings which avoid a given set of patterns. Little research has been conducted regarding the word size required for a word to contain all patterns of a given set of patterns. The set of patterns for which containment is sought in this thesis is the set of preferential arrangements of a given length. The term preferential arrangement denotes strings of characters in which repeated characters are allowed, but not necessary. Cardinalities for sets of all preferential arrangem

APA, Harvard, Vancouver, ISO, and other styles

47

Lane, Stephen M. "Trees with Unique Minimum Locating-Dominating Sets." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2196.

Full text

Abstract:

A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.

APA, Harvard, Vancouver, ISO, and other styles

48

Holmes, Kristin Renee Stone. "Locating-Domination in Complementary Prisms." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1871.

Full text

Abstract:

Let G = (V (G), E(G)) be a graph and G̅ be the complement of G. The complementary prism of G, denoted GG̅, is the graph formed from the disjoint union of G and G̅ by adding the edges of a perfect matching between the corresponding vertices of G and G̅. A set D ⊆ V (G) is a locating-dominating set of G if for every u ∈ V (G)D, its neighborhood N(u)⋂D is nonempty and distinct from N(v)⋂D for all v ∈ V (G)D where v ≠ u. The locating-domination number of G is the minimum cardinality of a locating-dominating set of G. In this thesis, we study the locating-domination number of complementary prisms.

APA, Harvard, Vancouver, ISO, and other styles

49

Cantrell, Daniel Shelton. "Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1872.

Full text

Abstract:

In this paper, we consider decompositions of the complete graph on v vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of: (1) a single cycle of length v, (2) f fixed points and a cycle of length v − f, or (3) two disjoint cycles. The purpose of this thesis is to give necessary and sufficient conditions for the existence of cyclic, f-cyclic, and bicyclic Q-decompositions of Kv.

APA, Harvard, Vancouver, ISO, and other styles

50

Wooten, Trina Marcella. "Finding Edge and Vertex Induced Cycles within Circulants." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/1985.

Full text

Abstract:

Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As a cycle with at least four vertices is a canonical example of a triangle-free subgraph, we concentrate our efforts on

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!