Relevant bibliographies by topics / Discrete Mathematics and Combinatorics

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Discrete Mathematics and Combinatorics'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Discrete Mathematics and Combinatorics"

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G., Rajkumar, and V. Ramadoss Dr. "A STUDY ON COMBINATORICS INDISCRETE MATHEMATICS." International Journal of Computational Research and Development 3, no. 2 (2018): 11–13. https://doi.org/10.5281/zenodo.1401389.

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Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly tho
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Litwiller, Bonnie H., and David R. Duncan. "Combinatorics Connections: Playoff Series and Pascal's Triangle." Mathematics Teacher 85, no. 7 (1992): 532–35. http://dx.doi.org/10.5951/mt.85.7.0532.

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One major theme of the National Council of Teachers of Mathematic's Curriculum and Evaluation Standards far School Mathematics (1989) is the connection between mathematical ideas and their applications to real-world situations. We shall use concepts from discrete mathematics in describing the relationship between sports series and Pascal's triangle.
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Walker, Richard, and Steven Skiena. "Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica." Mathematical Gazette 76, no. 476 (1992): 286. http://dx.doi.org/10.2307/3619148.

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Mohite, Neeta Ravindra, and Dr G. J. Chhajed. "A Review of Discrete Mathematics in Artificial Intelligence." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 09, no. 01 (2025): 1–9. https://doi.org/10.55041/ijsrem40438.

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- The foundation of many Artificial Intelligence (AI) approaches and algorithms is discrete mathematics. Graph theory, combinatorics, and logic are just a few of the discrete mathematics fields that provide substantial contributions to AI. Each of these fields is essential to the development of contemporary AI systems. This section lays the groundwork for a more in-depth examination of particular instances by giving a summary of how discrete mathematics supports the architecture and operation of AI Key Words: Artificial Intelligence, Discrete Mathematics, Graph Theory, Combinatorics in AI.
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Tarlow, Lynn D. "Sense-able Combinatorics: Students' Use of Personal Representations." Mathematics Teaching in the Middle School 13, no. 8 (2008): 484–89. http://dx.doi.org/10.5951/mtms.13.8.0484.

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As we move forward in the twenty-first century, information and its communication have become at least as important as the production of material goods, and the nonmaterial world of information processing requires the use of discrete mathematics (NCTM 1989). Combinatorics, the mathematics of counting, plays a significant role in discrete mathematics. It is usually described as having three parts: counting (how many things meet our description), optimization (which is the best), and existence (are there any at all). The NCTM is explicit about the importance of students learning discrete mathema
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Bala, Romi, and Hemant Pandey. "Advances in Discrete Mathematics: From Combinatorics to Cryptography." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 3 (2019): 1643–46. http://dx.doi.org/10.61841/turcomat.v10i3.14624.

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Discrete mathematics forms the foundation for various fields, including computer science and cryptography, by providing essential tools for problem-solving in discrete structures. This paper explores the advancements in discrete mathematics, focusing on combinatorics and cryptography. It discusses the basic concepts of combinatorics, such as permutations, combinations, and graph theory, along with their applications in modern cryptography. The paper also examines symmetric and public key cryptography algorithms, including DES, AES, RSA, and ECC, highlighting their key features and security mec
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Dr., Mohd. Rizwanullah. "HISTORY OF COMBINATORIAL OPTIMIZATION: STUDY OF AN APPLICATION BASED NETWORK FLOWS." International Journal of Pure & Applied Mathematical Research 1, no. 1 (2017): 36–41. https://doi.org/10.5281/zenodo.10823935.

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Abstract -<strong><em> </em></strong><em>Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. Combinatorial theory (or combinatorial analysis) is concerned with problems of enumeration and structure of mathematical objects. The objects may represent physical situation or things in applications or may be purely abstract and under study for theoretical reason. It is common practice to refer to the subject matter of combinatorial theory as combinatorics. The availability of reliable software, extremely fast and inexpensive hardware This pape
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Kung, Joseph P. S. "Combinatorics and Nonparametric mathematics." Annals of Combinatorics 1, no. 1 (1997): 105–6. http://dx.doi.org/10.1007/bf02558467.

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Adiprasito, Karim, Xavier Goaoc, and Zuzana Patáková. "Discrete Geometry." Oberwolfach Reports 21, no. 1 (2024): 137–202. http://dx.doi.org/10.4171/owr/2024/3.

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A number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as convex geometry, combinatorics, or topology. Two open problem sessions highlighted the abundance of open questions and many of the results presented were obtained by young researchers, confirming the vitality of the field.
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Annamalai, Chinnaraji. "Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions." Journal of Engineering and Exact Sciences 8, no. 7 (2022): 14648–01. http://dx.doi.org/10.18540/jcecvl8iss7pp14648-01i.

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Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and computational equations for solving today’s scientific problems and challenges. This paper presents combinatorial geometric series, innovative binomial coefficients, combinatorial equations, binomial expansions, calculus with combinatorial geometric series, and innovative binomial theorems. Combinatorics involves integers, factorials, binomial coefficients, discrete mathematics, and theoretical computer science for finding solutions to the problems in computing and engineerin
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Dissertations / Theses on the topic "Discrete Mathematics and Combinatorics"

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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.

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

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

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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
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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.

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

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

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

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

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

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

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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
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Books on the topic "Discrete Mathematics and Combinatorics"

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Jerome, Lewis, and Saylor O. Dale, eds. Discrete mathematics with combinatorics. 2nd ed. Pearson Education, 2004.

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Skiena, Steven S. Implementing discrete mathematics: Combinatorics and graph theory with Mathematica. Addison-Wesley, 1990.

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Habib, Michel. Probabilistic Methods for Algorithmic Discrete Mathematics. Springer Berlin Heidelberg, 1998.

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Ferland, Kevin K. Discrete mathematics: An introduction to proofs and combinatorics. Houghton Mifflin Co., 2009.

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Berthé, V., and Michel Rigo. Combinatorics, words and symbolic dynamics. Cambridge University Press, 2015.

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Hillman, Abraham P. Discrete and combinatorial mathematics. Dellen, 1987.

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Grimaldi, Ralph P. Discrete and combinatorial mathematics. Addison-Wesley Pub. Co., 1985.

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Grimaldi, Ralph P. Discrete and combinatorial mathematics. Addison-Wesley Publ, 1989.

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Gavrilov, G. P. Problems and Exercises in Discrete Mathematics. Springer Netherlands, 1996.

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Benjamin, Arthur. Discrete mathematics. The Teaching Company, 2009.

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Book chapters on the topic "Discrete Mathematics and Combinatorics"

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Lovász, L., J. Pelikán, and K. Vesztergombi. "Combinatorics in Geometry." In Discrete Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21777-0_11.

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Grossman, Peter. "Combinatorics." In Discrete Mathematics for Computing. Macmillan Education UK, 1995. http://dx.doi.org/10.1007/978-1-349-13908-8_9.

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Grossman, Peter. "Combinatorics." In Discrete Mathematics for Computing. Macmillan Education UK, 2009. http://dx.doi.org/10.1007/978-0-230-37405-8_9.

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Yadav, Santosh Kumar. "Basic Combinatorics." In Discrete Mathematics with Graph Theory. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-21321-2_2.

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Senthil Kumar, B. V., and Hemen Dutta. "Combinatorics." In Discrete Mathematical Structures. CRC Press, 2019. http://dx.doi.org/10.1201/9780429053689-2.

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Baxter, Nancy, Ed Dubinsky, and Gary Levin. "Combinatorics, Matrices, Determinants." In Learning Discrete Mathematics with ISETL. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3592-7_6.

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Sridharan, Sriraman, and R. Balakrishnan. "Combinatorics." In Foundations of Discrete Mathematics with Algorithms and Programming. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781351019149-2.

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Lovász, L., J. Pelikán, and K. Vesztergombi. "Combinatorial Tools." In Discrete Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21777-0_2.

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Lovász, L., J. Pelikán, and K. Vesztergombi. "Combinatorial Probability." In Discrete Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21777-0_5.

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McDiarmid, C. "Discrete Mathematics and Radio Channel Assignment." In Recent Advances in Algorithms and Combinatorics. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22444-0_2.

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Conference papers on the topic "Discrete Mathematics and Combinatorics"

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Peng, Zhuogang, and Ryan McClarren. "A Low-Rank Method for the Discrete Ordinate Transport Equation Compatible With Transport Sweeps." In Mathematics and Computation 2021. American Nuclear Society, 2021. https://doi.org/10.13182/xyz-33829.

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Tabera Alonso, Luis Felipe. "Discrete Mathematics Days 2022." In Discrete Mathematics Days 2022. Editorial Universidad de Cantabria, 2022. http://dx.doi.org/10.22429/euc2022.016.

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The Discrete Mathematics Days (DMD20/22) will be held on July 4-6, 2022, at Facultad de Ciencias of the Universidad de Cantabria (Santander, Spain). The main focus of this international conference is on current topics in Discrete Mathematics, including (but not limited to): • Algorithms and Complexity • Combinatorics • Coding Theory • Cryptography • Discrete and Computational Geometry • Discrete Optimization • Graph Theory • Location and Related Problems The previous editions were held in Sevilla in 2018 and in Barcelona in 2016, inheriting the tradition of the Jornadas de Matemática Discreta
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Malheiros, Marcelo De Gomensoro, and Claus Haetinger. "Explorable Discrete Mathematics: a Python-based undergraduate-level teaching approach." In Simpósio Brasileiro de Informática na Educação. Sociedade Brasileira de Computação - SBC, 2024. http://dx.doi.org/10.5753/sbie.2024.242630.

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Discrete Mathematics is a foundational yet demanding introductory subject for Computer Science curricula, where undergraduate students typically have difficulties grasping its concepts and applications. In this work, we describe our teaching approach, using a programming language in tandem with math notation, inviting students to explore and learn its main concepts. Our goal is to build intuition through experimentation: first, evaluating expressions and running code snippets, then linking the programming constructs to mathematical notation, and finally, formalizing the underlying theory. For
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Fernández, Nicolás, Jaime García-García, Elizabeth Arredondo, and Isaac Imilpán. "Knowledge of Binomial Distribution in Pre-service Mathematics Teachers." In Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. International Association for Statistical Education, 2022. http://dx.doi.org/10.52041/iase.icots11.t8b2.

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The binomial distribution is one of the most important discrete distributions in probability and statistics; however, research identifies weaknesses in teachers’ and students’ application of binomial distributions for solving tasks beyond the direct use of the formula. Based on historical epistemological study and notions from the onto-semiotic approach to mathematical knowledge and instruction, we designed and administered a questionnaire to secondary school mathematics teachers in training. In our results, we identify and describe a lack of articulation among historical epistemological eleme
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Kutsenko, Alexander Vladimirovich. "New constructions and lower bound of number of self-dual bent functions." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-85.

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The paper considers maximally non-linear Boolean functions of even number of variables - bent functions. These functions have a number applications in coding theory and cryptography. For each bent function, the dual to it bent functions. A bent function is called self-dual if it coincides with its dual. Characteristic vectors of self-dual bent functions are eigenvectors of the matrix Sylvester-Hadamard, which has applications in combinatorics, theory signals and quantum computing. The paper proposes a number of new iterative constructions of self-dual bent functions of n variables, in within w
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Gasparyan, Armenak Sokratovich. "Combinatorial identities over recurrent sequences." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-45.

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The article presents several general identities, special cases which are many well-known identities such as, for example, Cassini, Catalan, Taguiri identities for Fibonacci numbers, their analogues and generalizations to other Fibonacci-type numbers.
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Rosen, David W. "Design of Modular Product Architectures in Discrete Design Spaces Subject to Life Cycle Issues." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1485.

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Abstract A product’s architecture affects the ability of a company to customize, assemble, service, and recycle the product. Much of the flexibility to address these issues is locked into the product’s design during the configuration design stage when the architecture is determined. The concepts of modules and modularity are central to the description of an architecture, where a module is a set of components that share some characteristic. Modularity is a measure of the correspondence between the modules of a product from different viewpoints, such as functionality and physical structure. The
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Corbett, Brian P., and David W. Rosen. "Platform Commonization With Discrete Design Spaces: Introduction of the Flow Design Space." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dtm-48678.

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Many companies have adopted the usage of common platforms to support the development of product families. The problem addressed in this paper deals with the development of a common platform for an existing set of products that may or may not already form a product family. The common platform embodies the core function, form, and technology base shared across the product family. In this work, we focus on configuration aspects of the platform commonization problem to determine which components are in the platform and the relationships among these components. Configuration design spaces are discr
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Sanjuan, E., M. Parra, and I. Castro. "Multimedia tools for the teaching of probability and statistics." In Statistics and the Internet. International Association for Statistical Education, 2003. http://dx.doi.org/10.52041/srap.03312.

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As it is well known, understanding some concepts is not a trivial task for a beginner in the field of the Probability and Statistics. With many students, they are initially greeted with mixed feelings of fear and anger. These feelings inhibit the learning of the probability and statistics. Emphasis has been placed in different directions with respect to the teaching of probability and statistics. Firstly, it focused on reducing the effort needed to perform statistical computations, but gave little insight into the meaning of concepts. Secondly, the emphasis was on meaning, but many of the stud
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Bokut, Leonid A. "My life in mathematics, 60 years." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0002.

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Reports on the topic "Discrete Mathematics and Combinatorics"

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Hammer, Peter L. Discrete Applied Mathematics. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada273552.

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Chau, Herman, Helen Jenne, Davis Brown, Sara Billey, Mark Raugas, and Henry Kvinge. Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research. Office of Scientific and Technical Information (OSTI), 2024. http://dx.doi.org/10.2172/2476539.

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Barnett, Janet, Guram Bezhanishvili, Hing Leung, et al. Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003984.

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Mhaskar, Hrushikesh N. Research Area 3: Mathematical Sciences: 3.4, Discrete Mathematics and Computer Science. Defense Technical Information Center, 2015. http://dx.doi.org/10.21236/ada625542.

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Pengelley, David. Sums of Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003986.

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Fellows, M. R. Research on Mega-Math: Discrete mathematics and computer science for children. Final report. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/106599.

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Hedetniemi, S. T., and R. Lasker. Clemson Mini-Conference onR discrete Mathematics (5th), Held in Clemson, South Carolina on October 11-12, 1990. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada238616.

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