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Journal articles on the topic 'Combinatorics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Mazza, Giordano. "The Secrets of Calvino's Ars Combinatoria." Italica 99, no. 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, com

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2

Gerards, A. M. H., and A. W. J. Kolen. "Polyhedral Combinatorics in Combinatorial Optimization." Statistica Neerlandica 41, no. 1 (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 (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 quit

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4

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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5

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 (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. Direciona

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6

Pak, Igor, and Colleen Robichaux. "Signed combinatorial interpretations in algebraic combinatorics." Algebraic Combinatorics 8, no. 2 (2025): 495–519. https://doi.org/10.5802/alco.413.

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We prove the existence of signed combinatorial interpretations for several large families of structure constants. These families include standard bases of symmetric and quasisymmetric polynomials, as well as various bases in Schubert theory. The results are stated in the language of computational complexity, while the proofs are based on the effective Möbius inversion.

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7

Bilkis, Cahaya, Martini, Muchamad Subali Noto, and Irmawati Liliyana Kusuma Dewi. "Uncovering the Secrets Behind Enumeration Rules: The Art of Combinatorics Thinking." International Journal of Educational Research Excellence (IJERE) 3, no. 2 (2024): 905–11. https://doi.org/10.55299/ijere.v3i2.1154.

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This research aims to analyze students' combinatorial thinking skills after using learning worksheets on enumeration rules. This research aims to provide solutions by applying learning materials to improve students' combinatorial thinking skills in solving math problems. The research method used is qualitative research. The research technique in this case is to use data triangulation. The purpose of triangulation is to increase the validity and reliability of research findings by confirming or complementing findings from various sources or perspectives. The results in this study are the divers

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8

Mardiningsih, Saib Suwilo, and Ihda Hasbiyati. "Existence of Polynomial Combinatorics Graph Solution." Journal of Research in Mathematics Trends and Technology 2, no. 1 (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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9

Patimo, Leonardo, and Jacinta Torres. "Atoms and charge in type C 2." Algebraic Combinatorics 8, no. 2 (2025): 521–74. https://doi.org/10.5802/alco.411.

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We construct atomic decompositions for crystals of type C 2 and use them to define a charge statistic, thus providing positive combinatorial formulas for the corresponding Kostka–Foulkes polynomials. Our methods include Kashiwara–Nakashima tableaux combinatorics as well as the combinatorics of string polytopes and twisted Bruhat graphs.

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10

HINKLE, BENJAMIN. "Parabolic limits of renormalization." Ergodic Theory and Dynamical Systems 20, no. 1 (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 limi

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11

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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12

Zhou, Sanming. "Congressus Numerantium: A new beginning." Congressus Numerantium 235 (January 11, 2025): 3–4. https://doi.org/10.61091/cn235-01.

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Congressus Numerantium (CN) is an esteemed international journal with a long history of publishing high-quality papers in combinatorics and related areas. Founded by the late Professor Ralph Gordon Stanton and with its first volume appeared in 1970, CN began with a series of conference proceedings in mathematics, but later it also published regular contributions directly submitted to the journal. In the past over 50 years, a large number of conferences published their proceedings in CN. Among them the first ones include: Southeastern Conference on Combinatorics, Graph Theory, and Computing; Lo

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13

Alova, Chard Aye. "Combinatorics in Vedic Mathematics." La Sallianum Ars et Scientia 1, no. 1 (2020): 98–117. http://dx.doi.org/10.70228/cbj2021014.

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This paper draws inspiration from the seminal work and great book of Bharati Krishna Tirthaji and the preceding contributions and significant contributions of Kenneth Williams, Swati Dave, Marianne Fletcher, James Glover, Veronica Prudente, Virgillo Prudente and Gowri Ramachandran. This research paper or study delves and works into the intriguing intersection and connection between Vedic Mathematics and Combinatorics, with a particular focus on permutations with repetition, permutations without repetition, combinations with repetition, and combinations without repetition. The study showcases t

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14

Seaman, Bill. "Oulipo | vs | Recombinant Poetics." Leonardo 34, no. 5 (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 i

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15

MINASYAN, ANGELA. "METHODOLOGY OF TEACHING ELEMENTS OF COMBINATORICS AT THE COMPREHENSIVE SECONDARY SCHOOL." Scientific bulletin 1, no. 46 (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

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16

Lecouvey, Cédric, and Cristian Lenart. "Combinatorics of Generalized Exponents." International Mathematics Research Notices 2020, no. 16 (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 pr

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17

Shelah, Saharon, and Lee J. Stanley. "The combinatorics of combinatorial coding by a real." Journal of Symbolic Logic 60, no. 1 (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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18

Ďuriš, Viliam, Gabriela Pavlovičová, Dalibor Gonda, and Anna Tirpáková. "Teaching Combinatorial Principles Using Relations through the Placemat Method." Mathematics 9, no. 15 (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 presen

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19

Rocha, Cristiane de Arimatéa, and Antonio Carlos de Souza. "The construction of Combinatorics concepts evidenced in mind maps." Revista Internacional de Pesquisa em Educação Matemática 14, no. 3 (2024): 1–18. https://doi.org/10.37001/ripem.v14i3.3818.

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Innovations in teaching practices in higher education are fundamental to promoting opportunities for students to engage in their training process. This study investigated the use of mind maps as an innovative pedagogical practice for the construction of concepts about combinatorics by maths undergraduates. Twenty-five groups of students from a Maths degree course took part in the research, taking an elective subject on the teaching of combinatorics. As a result, it was observed that the different constructions of mind maps provide indications of the breadth, depth and personal notions of combi

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20

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 nec

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21

Semanišinová, Ingrid. "Multiple-Solution Tasks in Pre-Service Teachers Course on Combinatorics." Mathematics 9, no. 18 (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,

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22

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

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23

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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24

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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25

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

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26

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

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27

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

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28

Markel, William D. "Cribbage: An Excellent Exercise in Combinatorial Thinking." Mathematics Teacher 98, no. 8 (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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29

Xiao, Ming. "Borel Chain Conditions of Borel Posets." Mathematics 11, no. 15 (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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30

Mas'ud, Syamsuddin. "Pendampingan Persiapan ONMIPA-PT 2023 Bidang Matematika pada Materi Kombinatorik bagi Mahasiswa Universitas Fajar." Jurnal Hasil-Hasil Pengabdian dan Pemberdayaan Masyarakat 2, no. 2 (2023): 279–83. https://doi.org/10.35580/jhp2m.v2i2.697.

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The preparation assistance for Olimpiade Nasional Matematika dan IPA – Perguran Tinggi (ONMIPA-PT) 2023 in the field of mathematics is an effort to enhance the mathematical skills of students so they can compete in the competition organized by the Ministry of Education, Culture, Research, and Technology. This assistance is considered necessary because the Universitas Fajar itself does not have a specific mathematics-related program of study. The assistance provided includes giving combinatorics material to selected Universitas Fajar students. Additionally, students are given practice to sharpe

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31

Edmonds, Allan L., and Steven Klee. "The Combinatorics of Hyperbolized Manifolds." MATHEMATICA SCANDINAVICA 117, no. 1 (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 rela

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32

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

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33

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 (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 thin

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34

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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35

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 dynami

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36

Borot, Gaëtan, Samuel Grushevsky, and Martin Möller. "Riemann Surfaces: Random, Flat, and Hyperbolic Geometry." Oberwolfach Reports 21, no. 3 (2025): 2369–424. https://doi.org/10.4171/owr/2024/41.

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This workshop brought together experts in Riemann surfaces from the point of view of hyperbolic geometry, experts on flat surfaces from the point of view of Teichmüller dynamics, and the combinatorics and probability community working on asymptotic properties, to focus on asymptotic behavior of Riemann surfaces and their combinatorial models at large genus.

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37

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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38

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 (2024): 31–46. http://dx.doi.org/10.56827/seajmms.2024.2001.3.

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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

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39

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

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40

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

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41

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

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42

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

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43

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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44

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

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45

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

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46

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

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47

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

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48

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

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49

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

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50

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

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