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Dissertations / Theses on the topic 'Catalan Numbers'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

An, Junkyu. "Combinatorial enumeration of weighted Catalan numbers." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/64609.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 69-70).<br>This thesis is devoted to the divisibility property of weighted Catalan and Motzkin numbers and its applications. In Chapter 1, the definitions and properties of weighted Catalan and Motzkin numbers are introduced. Chapter 2 studies Wilf conjecture on the complementary Bell number, the alternating sum of the Stirling number of the second kind. Congruence properties of the complementary Bell numbers are found by weight

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2

Richardson, Steven L. "Enumeration of the generalized Catalan numbers." Morgantown, W. Va. : [West Virginia University Libraries], 2005. https://etd.wvu.edu/etd/controller.jsp?moduleName=documentdata&jsp%5FetdId=3906.

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3

Allen, Emily. "Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/366.

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The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of this interpretation in terms of Dyck paths. We then convert our weighted interpretation into a conven

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4

Mott, Brittany Nicole. "Analysis of the Generalized Catalan Orbits." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302396750.

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5

Guerrini, Veronica. "On enumeration sequences generalising Catalan and Baxter numbers." Doctoral thesis, Università di Siena, 2018. http://hdl.handle.net/11365/1035968.

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The study carried out along this dissertation fits into the field of enumerative combinatorics. The structures that have been investigated are families of discrete objects which display combinatorial properties. They are mainly subfamilies of well-known combinatorial structures, such as lattice paths, pattern-avoiding permutations, polyominoes (more specifically, parallelogram polyominoes), or inversion sequences. Furthermore, these combinatorial families are closely related to two famous number sequences known in the literature as the Catalan and Baxter numbers. We start defining and s

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6

Auger, Joseph Thomas. "Orbits of the Dissected Polygons of the Generalized Catalan Numbers." University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302701692.

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7

Loehr, Nicholas Anthony. "Multivariate analogues of Catalan numbers, parking functions, and their extensions /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3091333.

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8

Brasil, Junior Nelson Gomes 1989. "Bijeções envolvendo os números de Catalan." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307511.

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Orientador: José Plínio de Oliveira Santos<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-25T04:32:08Z (GMT). No. of bitstreams: 1 BrasilJunior_NelsonGomes_M.pdf: 980636 bytes, checksum: dd8d61baeb633d5f598abc3523def800 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, estudamos a sequência dos Números de Catalan, uma sequência que aparece como solução de vários problemas de contagem envolvendo árvores, palavras, grafos e outras estruturas combinatórias. Atualmente, são

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9

Drescher, Chelsea. "Invariants of Polynomials Modulo Frobenius Powers." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1703327/.

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Rational Catalan combinatorics connects various Catalan numbers to the representation theory of rational Cherednik algebras for Coxeter and complex reflection groups. Lewis, Reiner, and Stanton seek a theory of rational Catalan combinatorics for the general linear group over a finite field. The finite general linear group is a modular reflection group that behaves like a finite Coxeter group. They conjecture a Hilbert series for a space of invariants under the action of this group using (q,t)-binomial coefficients. They consider the finite general linear group acting on the quotient of a pol

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10

Valqui, Haase Christian Holger, and Marco Solórzano. "The Groebner basis of a polynomial system related to the Jacobian conjecture." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95235.

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We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.<br>En este artículo calculamos la base de Groebner de un sistema polinomial de ecuaciones relacionada con la conjetura del jacobiano utilizando una fórmula recursiva para los numeros de Catalan.

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11

Guichard, Christelle. "Les nombres de Catalan et le groupe modulaire PSL2(Z)." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAM057/document.

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Dans ce mémoire de thèse, on étudie le morphisme de monoïde $mu$du monoïde libre sur l'alphabet des entiers $nb$,`a valeurs dans le groupe modulaire $PSL_2(zb)$,considéré comme monoïde, défini pour tout entier $a$ par $mu(a)=begin{pmatrix} 0 & -1 1 & a+1 end{pmatrix}.$Les nombres de Catalan apparaissent naturellement dans l'étudede sous-ensembles du noyau de $mu$.Dans un premier temps, on met en évidence deux systèmes de réécriture, l'un sur l'alphabet fini ${0,1}$, l'autresur l'alphabet infini des entiers $nb$ et on montreque ces deux systèmes de réécriture définissent des présentatio

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12

Rasnick, Rebecca. "Generalizations of the Arcsine Distribution." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3565.

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The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first few flips.

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13

Veiga, Busto Raquel. "Person and number in Catalan Sign Language pronouns." Doctoral thesis, Universitat Pompeu Fabra, 2022. http://hdl.handle.net/10803/673364.

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Languages use different resources to specify the numerosity of the referents and to denote the speech act participants. This thesis describes the morphophonological strategies used in Catalan Sign Language (LSC) personal pronouns to encode these distinctions. In a nutshell, I argue that the expression of person and number is achieved by using two interrelated strategies: person is expressed through spatial features (locations in the signing space which are defined in relation to the signer’s body), number is grammatically marked by the path specifications of the sign (movements connect

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14

Rouyer, Julien. "Contribution à la gestion du trafic routier pour le véhicule connecté." Electronic Thesis or Diss., Reims, 2024. http://www.theses.fr/2024REIMS009.

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Nous étudions divers aspects des intersections routières : tout en présentant des propriétés combinatoires des trajets pouvant être empruntés simultanément pour les traverser, nous proposons un algorithme de consensus à destination de véhicules connectés, visant à abolir la nécessité de panneaux de signalisation et feux tricolores : les voies ouvertes à la circulation sont choisies en temps réel et l'information circule par le biais de CAM. Cet algorithme utilise une fonction qui, à chaque file d'attente, associe un poids : elle a été construite comme un optimum expérimental obtenu à partir d'

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15

Siegel, Aron Curtis. "Counting the Number of Distinct Dissections of a Regular N-Gon." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1396794759.

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16

GUIMARÃES, Hugo Leonardo de Andrade. "O PASSEIO DE CATALAN NA PRAIA E AS GRASSMANNIANAS DE RETAS." Universidade Federal de Pernambuco, 2012. https://repositorio.ufpe.br/handle/123456789/11688.

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Submitted by Etelvina Domingos (etelvina.domingos@ufpe.br) on 2015-03-10T17:09:30Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) HLAG.pdf: 1126552 bytes, checksum: 1e1ac46e79a77b1688e9cb1f88285609 (MD5)<br>Made available in DSpace on 2015-03-10T17:09:30Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) HLAG.pdf: 1126552 bytes, checksum: 1e1ac46e79a77b1688e9cb1f88285609 (MD5) Previous issue date: 2012-01<br>O objetivo desse trabalho é mostrar que os Top Intersection Numbers das Grassman

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17

Rondós, Elena. "Noves eines per a l'anàlisi sectorial. Aplicació al sector agrícola català." Doctoral thesis, Universitat de Girona, 2019. http://hdl.handle.net/10803/668335.

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This doctoral thesis aims at developing and implementing a computational framework for performing virtual testing of composite structures using a High-Performance Computing (HPC) environment. In this sense, this thesis presents several novel constitutive models based on the continuum damage mechanics theory and their implementation in the HPC-base Finite Element (FE) simulation code called Alya. The verification and validation of the models are performed comparing the numerical predictions with analytical formulations and experimental data. The comparisons demonstrate not only the reliability

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18

Garcia, Luciano de Oliveira. "Efeito do pH e dureza da água em juvenis de Rhamdia quelen infectados com Ichthyophthirius multifiliis (Fouquet, 1876)." Universidade Federal de Santa Maria, 2008. http://repositorio.ufsm.br/handle/1/4313.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The aim of this study was to determine the intensity of Ichthyophthirius multifiliis infection, as well as net ion fluxes (Na+, K+ and Cl-), in silver catfish juveniles exposed to different pHs (5, 6, 7, 8, and 9 for sixteen days), pH (5.0 and 7.0) and hardness (20, 60 and 120 mg CaCO3.L-1 for sixteen days) and the oxidative stress parameters in liver, gill and muscle of this species and submitted to different pH (5.0 and 7.0 for three days). Net Na+, K+, and Cl- fluxes were determined at different times, trophonts in the skin

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19

Wu, Hsin-Lieh, and 吳欣烈. "Catalan Numbers and Their Relative Numbers." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/76245016414143902856.

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碩士<br>國立交通大學<br>應用數學系所<br>103<br>There are many combinatorial structures counted by Catalan numbers. So far, many other applications relative to Catalan numbers are discussed, such as Narayana numbers and Motzkin numbers. In this thesis, we collect four combinatorial problems whose solutions with Catalan numbers involved. Some other numbers related to Catalan numbers are also investigated.

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20

Schumacher, Paul R. "Parking Functions And Generalized Catalan Numbers." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-853.

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Since their introduction by Konheim and Weiss, parking functions have evolved into objects of surprising combinatorial complexity for their simple definitions. First, we introduce these structures, give a brief history of their development and give a few basic theorems about their structure. Then we examine the internal structures of parking functions, focusing on the distribution of descents and inversions in parking functions. We develop a generalization to the Catalan numbers in order to count subsets of the parking functions. Later, we introduce a generalization to parking functions in the

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21

Tsai, Shiu-Kai, and 蔡旭凱. "Catalan Numbers: Problems and Their Bijective Relations." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/20513382846801007156.

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碩士<br>逢甲大學<br>應用數學學系<br>103<br>The thesis starts by introducing the history and formula on the Catalan numbers. Then some combinatorial problems are given and the answers of them are proved to be Catalan numbers. Finally, we find the bijective relations among these problems. The objective is to give a clear explanation and interesting correspondence thereof to those who first encounter the Catalan numbers.

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22

Michalik, Jindřich. "Kombinatorické posloupnosti čísel a dělitelnost." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-373204.

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This work contains an overview of the results concerning number-theoretic pro- perties of some significant combinatorial sequences such as factorials, binomial coef- ficients, Fibonacci and Catalan numbers. These properties include parity, primality, prime power divisibility, coprimality etc. A substantial part of the text should be accessible to gifted high school students, the results are illustrated with examples. 1

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23

Lee, Ing-Jye, and 李英杰. "A Bijective Proof of Catalan Number." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/58713391042282037077.

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24

Jui-HsiangChen and 陳瑞祥. "Two Special Types of Parking Functions Related to Catalan Number and Fine Number." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/8g6r74.

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碩士<br>國立成功大學<br>數學系應用數學碩博士班<br>107<br>We introduce two special types of parking function, V-parking function and Lambda-parking function, which are inspired by the unimodal sequence. Then, we prove the suprising facts that the number of V-parking functions are Catalan numbers and the number of Lambda-parking functions are Fine numbers. (In appendix A, we verify that the diagonal sums of Catalan triangle are Fine numbers by giving bijections.)

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