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Journal articles on the topic 'Combinatorics'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 October 2024

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1

Mazza, Giordano. "The Secrets of Calvino's Ars Combinatoria." Italica 99, no. 1 (March 1, 2022): 40–57. http://dx.doi.org/10.5406/23256672.99.1.04.

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Abstract In this article, I explore the relationship between secrets and ars combinatoria, or the art of combining elements.1 In particular, I analyze this relationship in Italo Calvino's works, as Calvino can be thought of as the major representative of combinatorial literature in Italy. Although there are several published articles discussing the literary theory on secrecy, and several more analyzing combinatorial literature in Calvino, none discusses the importance of secrets in Calvino or links combinatorial literature with secrecy. I argue that ars combinatoria and, more specifically, combinatorial literature, is always closely linked with secrecy. I demonstrate that secrecy is a key aspect of combinatorial literature and that such combinatory elements become an essential part of Calvino's storytelling. I first define each of these terms (secrecy and combinatorics) in a broader context and then in the context of their literary usage.

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2

Gerards, A. M. H., and A. W. J. Kolen. "Polyhedral Combinatorics in Combinatorial Optimization." Statistica Neerlandica 41, no. 1 (March 1987): 1–25. http://dx.doi.org/10.1111/j.1467-9574.1987.tb01168.x.

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3

MANDARIA, George. "The Methodology of Teaching Algorithms of Combinatorics: Permutations, Combinations, Arrangements." Journal of Technical Science and Technologies 7, no. 2 (December 15, 2018): 1–6. http://dx.doi.org/10.31578/jtst.v7i2.139.

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In this article we have described the methodology for teaching the algorithms of combinatorics which are often used when solving tasks of informatics. These are the economic types of tasks in which we need to select different objects, sort selected objects in some order and choose the best selection from all possible selections. The formulas of calculating number of such selections are known from mathematics, but in informatics we are interested not only in number, but also in selections themselves, which can be generated by special algorithms. In general, the number of such selections is quite large, so we need to use optimal algorithms to find the desired answer in real time. The essence of combinatoric objects is explained. It is shown how to find the desired object in optimal way. The samples and description of the corresponding algorithms are presented using the programming language C ++. Keywords: Combinatorics, Methodology, Permutations, Combinations, Arrangements, Combinatorial object, Selections

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4

Rocha, Cristiane Arimatéa, and Antonio Carlos De Souza. "Conhecimento de crianças pequenas da Educação Infantil e alunos dos anos iniciais do Ensino Fundamental sobre Combinatória: O que apontam as pesquisas brasileiras no período de 2010 a 2019?<br>Conocimiento de los niños pequeños en Educación Infantil y de los estudiantes de los primeros años de la escuela primaria sobre Combinatoria: ¿Qué señalan las investigaciones brasileñas en el período 2010-2019?" Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática 23, no. 4 (July 4, 2021): 452–84. http://dx.doi.org/10.23925/983-3156.2021v23i4p452-484.

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A presente investigação discorre sobre um recorte de um projeto que visa apresentar as pesquisas em Educação Estatística no Brasil publicadas em periódicos da área de Ensino entre os anos de 2010 a 2019. Definimos como objetivo, para esse recorte, discutir pesquisas brasileiras que abordam conhecimentos de crianças pequenas da Educação Infantil e alunos dos anos iniciais do Ensino Fundamental sobre Combinatória no período mencionado. Foram identificados oito trabalhos que tratam direta ou indiretamente sobre conhecimentos de combinatória dos estudantes dessas etapas de escolarização. Direcionamos nosso olhar para os problemas combinatórios utilizados nas pesquisas, ressaltando aspectos como os diferentes tipos de problemas, a ordem de grandeza adotada (número total de possibilidades), os contextos evidenciados pelos problemas, além dos recursos utilizados para apresentação das atividades aos participantes da pesquisa. Verificamos que as pesquisas brasileiras estão em consonância com as investigações dos diferentes países e apresentam um avanço no sentido de permitir a discussão, nessas etapas de escolarização, dos diferentes tipos de problemas combinatórios em um mesmo estudo. Consideramos a necessidade de que outras pesquisas sejam realizadas abordando a elaboração de argumentos pessoais na resolução de problemas combinatórios. The present investigation discusses an excerpt from a project that aims to discuss the research on Statistical Education in Brazil published in journals in the area of Mathematics Education between the years 2010 to 2019. We set the objective to discuss Brazilian research that addresses the knowledge of young children in kindergarten and students in the early years of elementary school about Combinatorics in this period. Eight papers were identified that deal directly or indirectly with combinatorics knowledge of students' in these schooling stages. We focused on the combinatorial problems used in the research, highlighting aspects such as the different types of problems, the order of magnitude adopted (total number of possibilities), the contexts evidenced by the problems, in addition to the resources used to present the activities to the research participants. We verified that Brazilian research is in line with the investigations from different countries and presents an advance in the sense of allowing the discussion of different types of combinatorial problems in the same study. We consider that further research should be conducted addressing the development of personal arguments in solving combinatorial problems. La presente investigación discute un extracto de un proyecto que tiene como objetivo presentar las investigaciones en Educación Estadística en Brasil, publicadas en revistas del área de Matemáticas Educativas entre los años 2010 y 2019. Nos fijamos como objetivo, para este extracto, discutir la investigación brasileña que aborda el conocimiento de los niños pequeños en Educación Infantil y de los estudiantes en los primeros años de la escuela primaria en Combinatoria en ese período de tiempo. Se identificaron ocho estudios que tratan directa o indirectamente el conocimiento combinatorio de los estudiantes de estas etapas de la escolarización. Centramos nuestra atención en los problemas combinatorios utilizados en las investigaciones, destacando aspectos como los diferentes tipos de problemas, el orden de magnitud adoptado (número total de posibilidades), los contextos evidenciados por los problemas, además de los recursos utilizados para presentar las actividades a los participantes de la investigación. Encontramos que la investigación brasileña está en línea con las investigaciones de diferentes países y presenta un avance en el sentido de permitir la discusión de diferentes tipos de problemas combinatorios en un mismo estudio. Consideramos la necesidad de que se realicen otras investigaciones que aborden la elaboración de argumentos personales en la solución de problemas combinatorios.

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5

Mardiningsih, Saib Suwilo, and Ihda Hasbiyati. "Existence of Polynomial Combinatorics Graph Solution." Journal of Research in Mathematics Trends and Technology 2, no. 1 (February 24, 2020): 7–13. http://dx.doi.org/10.32734/jormtt.v2i1.3755.

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The Polynomial Combinatorics comes from optimization problem combinatorial in form the nonlinear and integer programming. This paper present a condition such that the polynomial combinatorics has solution. Existence of optimum value will be found by restriction of decision variable and properties of feasible solution set or polyhedra.

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6

Tao, Terence. "Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory." EMS Surveys in Mathematical Sciences 1, no. 1 (2014): 1–46. http://dx.doi.org/10.4171/emss/1.

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7

HINKLE, BENJAMIN. "Parabolic limits of renormalization." Ergodic Theory and Dynamical Systems 20, no. 1 (February 2000): 173–229. http://dx.doi.org/10.1017/s0143385700000092.

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A unimodal map $f:[0,1] \to [0,1]$ is renormalizable if there is a sub-interval $I \subset [0,1]$ and an $n > 1$ such that $f^n|_I$ is unimodal. The renormalization of $f$ is $f^n|_I$ rescaled to the unit interval.We extend the well-known classification of limits of renormalization of unimodal maps with bounded combinatorics to a classification of the limits of renormalization of unimodal maps with essentially bounded combinatorics. Together with results of Lyubich on the limits of renormalization with essentially unbounded combinatorics, this completes the combinatorial description of limits of renormalization. The techniques are based on the towers of McMullen and on the local analysis around perturbed parabolic points. We define a parabolic tower to be a sequence of unimodal maps related by renormalization or parabolic renormalization. We state and prove the combinatorial rigidity of bi-infinite parabolic towers with complex bounds and essentially bounded combinatorics, which implies the main theorem.As an example we construct a natural unbounded analogue of the period-doubling fixed point of renormalization, called the essentially period-tripling fixed point.

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8

Lecouvey, Cédric, and Cristian Lenart. "Combinatorics of Generalized Exponents." International Mathematics Research Notices 2020, no. 16 (July 5, 2018): 4942–92. http://dx.doi.org/10.1093/imrn/rny157.

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Abstract We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type $A_{n-1}$, we rederive the description of the generalized exponents in terms of crystal graphs without using the combinatorics of semistandard tableaux or the charge statistic. In finite type $C_{n}$, we obtain a combinatorial description of the generalized exponents based on the so-called distinguished vertices in crystals of type $A_{2n-1}$, which we also connect to symplectic King tableaux. This gives a combinatorial proof of the positivity of Lusztig $t$-analogs associated to zero-weight spaces in the irreducible representations of symplectic Lie algebras. We also present three applications of our combinatorial formula and discuss some implications to relating two type $C$ branching rules. Our methods are expected to extend to the orthogonal types.

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9

Shelah, Saharon, and Lee J. Stanley. "The combinatorics of combinatorial coding by a real." Journal of Symbolic Logic 60, no. 1 (March 1995): 36–57. http://dx.doi.org/10.2307/2275508.

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AbstractWe lay the combinatorial foundations for [5] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.

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10

Seaman, Bill. "Oulipo | vs | Recombinant Poetics." Leonardo 34, no. 5 (October 2001): 423–30. http://dx.doi.org/10.1162/002409401753521548.

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This paper compares and contrasts approaches to combinatorics in OULIPO and Recombinant Poetics. OULIPO, also known as Ouvroir de Litérature Potentielle, is a literary and artistic association founded in the 1960s whose combinatoric methods and experimental concepts continue to be generative and relevant to this day. Recombinant Poetics is a term that I coined in 1995 in order to define a particular approach to emergent meaning that is used in generative virtual environments and other computer-based combinatoric media forms. Combinatoric works enable the exploration of sets of media elements in different orders and combinations. The meaning of such work is derived through dynamic interaction. Another group exploring combinatorics uses digital audio techniques. The abbreviation “VS” (“versus”) is often used in techno-audio remix culture to designate the remix of one group's music by another, often having only an oblique relation to the original.

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11

MINASYAN, ANGELA. "METHODOLOGY OF TEACHING ELEMENTS OF COMBINATORICS AT THE COMPREHENSIVE SECONDARY SCHOOL." Scientific bulletin 1, no. 46 (April 26, 2024): 99–110. http://dx.doi.org/10.24234/scientific.v1i46.138.

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The object of the study is the elements of combinatorics at the comprehensive secondary school. The aim of the article is to improve the methodological system of teaching elements of combinatorics at the comprehensive secondary school. The article discusses methodological issues and problems of studying combinatorics elements in the process of teaching mathematics. The methodological features of studying combinatorics elements at the comprehensive secondary school are identified and characterized, their role in the course of mathematics from the point of view of improving the effectiveness of learning is considered. The methods and methodical techniques of teaching combinatorial material, which were previously tested in our educational process, are presented. The possibilities and expediency of their application in connection with the age peculiarities of students are substantiated. Methodological guidelines for teaching individual topics of combinatorics are given. Within the framework of teaching each topic, interesting tasks of applied significance are presented. Effective methods of their solution are given. The presented tasks have been tested for years in our teaching practice. In the process of teaching the elements of combinatorics, methods of cooperative learning, mathematical modeling, graphical modeling, coding, methods that promoting inter- and intra-subject connections were used.

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12

Ďuriš, Viliam, Gabriela Pavlovičová, Dalibor Gonda, and Anna Tirpáková. "Teaching Combinatorial Principles Using Relations through the Placemat Method." Mathematics 9, no. 15 (August 2, 2021): 1825. http://dx.doi.org/10.3390/math9151825.

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The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach.

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13

DYDYK-MEUSH, Hanna. "COMPATIBILITY VS COMBINATORICS FOR THE DEVELOPMENT OF THE HISTORY OF UKRAINIAN LANGUAGE." Ukraine: Cultural Heritage, National Identity, Statehood 32 (2019): 293–303. http://dx.doi.org/10.33402/ukr.2019-32-293-303.

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The relevance of the studies is due to the need for a comprehensive analysis of compatibility in the Ukrainian language according to written sources of the 16th–18th centuries; special attention is paid to the causes of the emergence and formation of combinatorial connections on the example of adjective-substantive word combinations. The study of combinatorics in the Ukrainian language of the 16th–18th centuries based on one-type phrases actualizes in the future the need to compare lexical-syntactic combinatorial changes in the Ukrainian language at different stages of its development as a necessary condition for creating a synthetic study on compatibility. The scientific novelty of the thesis is that the first time combinatorics (compatibility) in the Ukrainian language of the 16th–18th centuries was studied comprehensively on the basis of combinatorial linguistics in combination with cognitive linguistics, substantive phrases. In this paper, for the first time, a scale of combinatorial (compositional) semantics was proposed for analyzing the compatibility in diachrony; for the first time, the principles of the combinatorial dictionary of the Ukrainian language of the 16th–18th centuries were developed. Keywords the monuments of writing, сompatibility, сombinatorics, active compatibility, passive compatibility, phrase.

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14

Semanišinová, Ingrid. "Multiple-Solution Tasks in Pre-Service Teachers Course on Combinatorics." Mathematics 9, no. 18 (September 16, 2021): 2286. http://dx.doi.org/10.3390/math9182286.

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In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers’ specialized knowledge (MTSK) theoretical framework. The study was carried out over the standard course of a summer semester in 2021. The course was attended by 13 pre-service teachers (PSTs). It was carried out online, due to COVID-19 restrictions. Ten combinatorial multiple-solution tasks were assigned to the PSTs. Analyzing pre-service teachers solutions to these tasks, we sought the description and better understanding of the combinatorial knowledge of the topic from the perspective of MSTK. The results revealed some critical aspects of mathematical knowledge in combinatorics that pre-service teachers education should focus on.

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15

Biggs, N. L. "GEOMETRIC ALGORITHMS AND COMBINATORIAL OPTIMIZATION: (Algorithms and Combinatorics 2)." Bulletin of the London Mathematical Society 22, no. 2 (March 1990): 204–5. http://dx.doi.org/10.1112/blms/22.2.204.

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16

Kock, Anders. "Combinatorics of non-holonomous jets." Czechoslovak Mathematical Journal 35, no. 3 (1985): 419–28. http://dx.doi.org/10.21136/cmj.1985.102032.

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17

Kahn, Jeff, Angelika Steger, and Benjamin Sudakov. "Combinatorics." Oberwolfach Reports 11, no. 1 (2014): 5–90. http://dx.doi.org/10.4171/owr/2014/01.

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18

Kahn, Jeff, Angelika Steger, and Benjamin Sudakov. "Combinatorics." Oberwolfach Reports 14, no. 1 (January 2, 2018): 5–81. http://dx.doi.org/10.4171/owr/2017/1.

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19

Kahn, Jeff, Angelika Steger, and Benjamin Sudakov. "Combinatorics." Oberwolfach Reports 17, no. 1 (February 9, 2021): 6–89. http://dx.doi.org/10.4171/owr/2020/1.

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20

Keevash, Peter, Wojciech Samotij, and Benny Sudakov. "Combinatorics." Oberwolfach Reports 20, no. 1 (October 6, 2023): 5–89. http://dx.doi.org/10.4171/owr/2023/1.

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21

Markel, William D. "Cribbage: An Excellent Exercise in Combinatorial Thinking." Mathematics Teacher 98, no. 8 (April 2005): 519–24. http://dx.doi.org/10.5951/mt.98.8.0519.

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Card games have long been a rich source of combinatorial exercises. Indeed, determining the probabilities of obtaining various hands in poker, and often in bridge, has been standard fare for elementary texts in both probability and combinatorics. Examples involving the game of cribbage, however, seem rare. This omission is especially surprising when one considers that cribbage hands offer excellent applications of combinatorial reasoning.

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22

Edmonds, Allan L., and Steven Klee. "The Combinatorics of Hyperbolized Manifolds." MATHEMATICA SCANDINAVICA 117, no. 1 (September 28, 2015): 31. http://dx.doi.org/10.7146/math.scand.a-22236.

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A topological version of a longstanding conjecture of H. Hopf, originally proposed by W. Thurston, states that the sign of the Euler characteristic of a closed aspherical manifold of dimension $d=2m$ depends only on the parity of $m$. Gromov defined several hyperbolization functors which produce an aspherical manifold from a given simplicial or cubical manifold. We investigate the combinatorics of several of these hyperbolizations and verify the Euler Characteristic Sign Conjecture for each of them. In addition, we explore further combinatorial properties of these hyperbolizations as they relate to several well-studied generating functions.

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23

Anderson, I. "COMBINATORICS Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability." Bulletin of the London Mathematical Society 19, no. 3 (May 1987): 273–75. http://dx.doi.org/10.1112/blms/19.3.273b.

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24

Xiao, Ming. "Borel Chain Conditions of Borel Posets." Mathematics 11, no. 15 (July 31, 2023): 3349. http://dx.doi.org/10.3390/math11153349.

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We study the coarse classification of partial orderings using chain conditions in the context of descriptive combinatorics. We show that (unlike the Borel counterpart of many other combinatorial notions), we have a strict hierarchy of different chain conditions, similar to the classical case.

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25

Frantzeskaki, Konstantina, Sonia Kafoussi, and Georgios Fessakis. "Developing Preschoolers’ Combinatorial Thinking with the Help of ICT: The Case of Arrangements." International Journal for Technology in Mathematics Education 27, no. 3 (September 1, 2020): 157–66. http://dx.doi.org/10.1564/tme_v27.3.04.

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In recent years, the learning and teaching of combinatorics presents particular educational research interest from the primary up to higher education levels. The combinatorial problems constitute a valuable opportunity for mathematical exploration, as combinatorics is a branch of mathematics with many applications, providing a complex network of connections with many areas of mathematics. The studies which examine the development of combinatorial thinking to preschoolers are limited. The purpose of this study is to investigate the effect of a microworld in the development of combinatorial thinking of kindergarten children. Specifically, the research concerns the production of arrangements two by two, three by two and four by two, from sets of discrete objects in the context of a digital microworld and embedded in a game and narrative context. The research findings show that the designed microworld comprises a developmentally appropriate learning environment for the meaningful learning and the development of combinatorial thinking by the preschoolers. The participants’ interaction with the microworld showed that the children can understand the concept of arrangement in a simulated concrete situation and that they can produce possible arrangements with various ability levels. A strong relation was revealed between the ability level of arrangements production of the children and their ability to pay attention to and interpret the feedback available in the microworld.

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26

Terekhov, D., T. T. Tran, D. G. Down, and J. C. Beck. "Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems." Journal of Artificial Intelligence Research 50 (July 22, 2014): 535–72. http://dx.doi.org/10.1613/jair.4278.

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Dynamic scheduling problems consist of both challenging combinatorics, as found in classical scheduling problems, and stochastics due to uncertainty about the arrival times, resource requirements, and processing times of jobs. To address these two challenges, we investigate the integration of queueing theory and scheduling. The former reasons about long-run stochastic system characteristics, whereas the latter typically deals with short-term combinatorics. We investigate two simple problems to isolate the core differences and potential synergies between the two approaches: a two-machine dynamic flowshop and a flexible queueing network. We show for the first time that stability, a fundamental characteristic in queueing theory, can be applied to approaches that periodically solve combinatorial scheduling problems. We empirically demonstrate that for a dynamic flowshop, the use of combinatorial reasoning has little impact on schedule quality beyond queueing approaches. In contrast, for the more complicated flexible queueing network, a novel algorithm that combines long-term guidance from queueing theory with short-term combinatorial decision making outperforms all other tested approaches. To our knowledge, this is the first time that such a hybrid of queueing theory and scheduling techniques has been proposed and evaluated.

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27

Bernabei, Maria Simonetta, and Horst Thaler. "Central Limit Theorem for Coloured Hard Dimers." Journal of Probability and Statistics 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/781681.

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We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.

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28

Blasiak, Pawel, Gérard H. E. Duchamp, and Karol A. Penson. "Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity." Advances in Mathematical Physics 2018 (October 22, 2018): 1–9. http://dx.doi.org/10.1155/2018/9575626.

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We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics. The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems.

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29

Fowler, John W. "Musical Combinatorics." Computer Music Journal 20, no. 1 (1996): 10. http://dx.doi.org/10.2307/3681260.

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30

Worboys, Mike, D. W. Stanton, and D. E. White. "Constructive Combinatorics." Mathematical Gazette 71, no. 458 (December 1987): 323. http://dx.doi.org/10.2307/3617076.

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31

Weber, Griffin, and Glenn Weber. "Pizza Combinatorics." College Mathematics Journal 26, no. 2 (March 1995): 141. http://dx.doi.org/10.2307/2687368.

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32

Bryant, Victor, and C. D. Godsil. "Algebraic Combinatorics." Mathematical Gazette 79, no. 484 (March 1995): 238. http://dx.doi.org/10.2307/3620119.

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33

Bousquet-Mélou, Mireille, Michael Drmota, Christian Krattenthaler, and Marc Noy. "Enumerative Combinatorics." Oberwolfach Reports 11, no. 1 (2014): 635–720. http://dx.doi.org/10.4171/owr/2014/12.

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34

Bousquet-Mélou, Mireille, Michael Drmota, Christian Krattenthaler, and Marc Noy. "Enumerative Combinatorics." Oberwolfach Reports 15, no. 2 (April 11, 2019): 1381–464. http://dx.doi.org/10.4171/owr/2018/23.

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35

Wild, P. "ALGEBRAIC COMBINATORICS." Bulletin of the London Mathematical Society 27, no. 2 (March 1995): 191–92. http://dx.doi.org/10.1112/blms/27.2.191.

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36

Goodall, G. W. "Probabilistic Combinatorics." Teaching Statistics 12, no. 2 (June 1990): 52–53. http://dx.doi.org/10.1111/j.1467-9639.1990.tb00107.x.

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37

Samarin, Victor I. "Fuzzy Combinatorics." Russian Journal of Mathematical Research. Series A 2, no. 2 (September 15, 2015): 45–57. http://dx.doi.org/10.13187/rjmr.a.2015.2.45.

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38

Farmaki, V., and S. Negrepontis. "Block combinatorics." Transactions of the American Mathematical Society 358, no. 6 (January 27, 2006): 2759–79. http://dx.doi.org/10.1090/s0002-9947-06-03864-5.

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39

Weber, Griffin, and Glenn Weber. "Pizza Combinatorics." College Mathematics Journal 26, no. 2 (March 1995): 141–43. http://dx.doi.org/10.1080/07468342.1995.11973685.

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40

Hirshfeld, Joram. "Nonstandard combinatorics." Studia Logica 47, no. 3 (September 1988): 221–32. http://dx.doi.org/10.1007/bf00370553.

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41

Blandín, Héctor, and Rafael Díaz. "Rational combinatorics." Advances in Applied Mathematics 40, no. 1 (January 2008): 107–26. http://dx.doi.org/10.1016/j.aam.2006.12.006.

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42

Charalambides, Charalambos A. "Enumerative combinatorics." ACM SIGACT News 39, no. 4 (November 30, 2008): 25–27. http://dx.doi.org/10.1145/1466390.1466395.

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43

Rincón, Felipe, Ngoc Mai Tran, and Josephine Yu. "Tropical Combinatorics." Notices of the American Mathematical Society 70, no. 01 (January 1, 2023): 1. http://dx.doi.org/10.1090/noti2597.

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44

Perelson, Alan S. "Applied combinatorics." Mathematical Biosciences 74, no. 1 (May 1985): 137. http://dx.doi.org/10.1016/0025-5564(85)90031-8.

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45

Hirschfeld, J. W. P. "Combinatorics 2010." Journal of Geometry 101, no. 1-2 (August 2011): 1. http://dx.doi.org/10.1007/s00022-011-0093-z.

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Not Available, Not Available. "Combinatorics 2002." Journal of Geometry 76, no. 1-2 (June 1, 2003): 1–2. http://dx.doi.org/10.1007/s00022-033-1113-4.

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Sinapova, Dima, and Spencer Unger. "Combinatorics atℵω." Annals of Pure and Applied Logic 165, no. 4 (April 2014): 996–1007. http://dx.doi.org/10.1016/j.apal.2013.12.001.

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Bousquet-Mélou, Mireille, Guillaume Chapuy, Michael Drmota, and Sergi Elizalde. "Enumerative Combinatorics." Oberwolfach Reports 19, no. 4 (July 26, 2023): 3215–305. http://dx.doi.org/10.4171/owr/2022/57.

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Blumberg, Andrew J., Michael A. Hill, Kyle Ormsby, Angélica M. Osorno, and Constanze Roitzheim. "Homotopical Combinatorics." Notices of the American Mathematical Society 71, no. 02 (February 1, 2024): 1. http://dx.doi.org/10.1090/noti2882.

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Khan, Waseem Ahmad, Ahmad Sarosh, and MD Jawed Miandad. "GENERALIZED DEGENERATE CHANGHEE-GENOCCHI NUMBERS AND POLYNOMIALS." South East Asian J. of Mathematics and Mathematical Sciences 20, no. 01 (April 30, 2024): 31–46. http://dx.doi.org/10.56827/seajmms.2024.2001.3.

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Abstract:

The degenerate Changhee-Genocchi numbers (and also Changhee - Genocchi), which appear in analysis and combinatorial mathematics and play a significant role in the applications and theory of mathematics, are associated with the Daehee, Cauchy, and Stirling numbers with several extensions and have proven to be powerful tools in varied subjects in combinatorics and analysis. In combinatorics and analytic number theory, many special numbers such as degenerate Changhee-Genocchi numbers, Changhee-Genocchi numbers, derangement numbers, and Stirling numbers play an important role to solve and analyze problems of combinatorial, analytical, and many other disciplines. In this paper, we introduce generalized degenerate Changhee-Genocchi polynomials and analyze some properties by providing several relations and applications. We first attain diverse relations and formulas covering addition formulas, recurrence rules, implicit summation formulas and relations with the earlier polynomials in the literature. By using their generating function, we derive some new relations including the Stirling numbers of the first and second kinds. Moreover, we introduce generalized higher-order degenerate Changhee-Genocchi polynomials. We also derive some new identities and properties of this type of polynomials.

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