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Journal articles on the topic 'Discrete Mathematics and Combinatorics'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

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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2

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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3

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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4

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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6

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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7

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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8

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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9

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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10

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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11

Reza Farahani, Mohammad, Mehdi Alaeiyan, Hayder Baqer Ameen, Xiujun Zhang, and Murat Cancan. "Applied Discrete Mathematics, Combinatorics, Cryptography, Computer Science and Computation." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 2 (2025): iii—iv. https://doi.org/10.47974/jdmsc-28-2-foreword.

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This special issue of “Applied Discrete Mathematics, Combinatorics, Cryptography, Computer Science and Computation”, presents a selection of cutting-edge research in the fields of cryptography, algebra, and module theory. These areas continue to evolve and provide foundational insights for modern technology, particularly in the realms of secure communication and mathematical modeling.

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12

Konvalina, John. "The Combinatorics of Discrete Self-Similarity." Advances in Applied Mathematics 19, no. 3 (1997): 415–28. http://dx.doi.org/10.1006/aama.1997.0556.

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13

Read, Ronald C. "Chemistry and discrete mathematics." Discrete Applied Mathematics 67, no. 1-3 (1996): 1–4. http://dx.doi.org/10.1016/0166-218x(95)00022-j.

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14

Posicelskaya, M. A. "CONSTRUCTIVE COMBINATORICS IN PRIMARY SCHOOL MATHEMATICS." Доклады Российской академии наук. Математика, информатика, процессы управления 511, no. 1 (2023): 66–94. http://dx.doi.org/10.31857/s2686954323700194.

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The paper is describing the class of educational problems from the course of mathematics and computer science for elementary school. This course has been implemented over the past decades by a team led by A.L. Semenov. In the problems it is required to find, build, list all objects that satisfy a certain system of conditions. The student conducts these activities in the visual world of the basic objects of discrete mathematics and computer science: strings (finite sequences of symbols), bags (multisets), tables, trees, and statements containing quantifiers. The connections of these problems wi

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15

Posicelskaya, M. A. "Constructive Combinatorics in Elementary School Mathematics." Doklady Mathematics 107, S1 (2023): S52—S77. http://dx.doi.org/10.1134/s106456242370059x.

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Abstract The paper describes in detail a class of educational problems from an elementary school course of mathematics and computer science. This course has been implemented over the past decades by a team led by Academician of the RAS A.L. Semenov. In the problems, it is necessary to find, build, or list all objects that satisfy a certain system of conditions. The student conducts these activities in a visual world of basic objects of discrete mathematics and computer science: strings (finite sequences of symbols), bags (multisets), tables, trees, and statements containing quantifiers. The co

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16

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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17

Shreeve, Richard I., and Ralph P. Grimaldi. "Discrete and Combinatorial Mathematics." Mathematical Gazette 81, no. 490 (1997): 163. http://dx.doi.org/10.2307/3618813.

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18

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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19

Ellington, Roni, James Wachira, and Asamoah Nkwanta. "RNA Secondary Structure Prediction by Using Discrete Mathematics: An Interdisciplinary Research Experience for Undergraduate Students." CBE—Life Sciences Education 9, no. 3 (2010): 348–56. http://dx.doi.org/10.1187/cbe.10-03-0036.

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The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete mathematical techniques and identifies specified base pairs as parameters. The goal of the REU was to introduce upper-level undergraduate students to the principles and challenges of interdisciplinary research in molecular biology and discrete ma

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20

González Yero, Ismael, and Juan Carlos Valenzuela Tripodoro. "10th Andalusian Meeting on Discrete Mathematics." Discrete Applied Mathematics 263 (June 2019): 1. http://dx.doi.org/10.1016/j.dam.2019.04.001.

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21

Munao, Simone. "Introducing article numbering to Discrete Mathematics." Discrete Mathematics 343, no. 1 (2020): 111754. http://dx.doi.org/10.1016/s0012-365x(19)30435-2.

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22

Uchôa-Filho, Bartolomeu F., and Cecilio Pimentel. "Enumerative Combinatorics and Shannon's Theory of Discrete Noiseless Channels." Electronic Notes in Discrete Mathematics 7 (April 2001): 118–21. http://dx.doi.org/10.1016/s1571-0653(04)00239-2.

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23

Chvátal, V. "Cutting Planes in Combinatorics." European Journal of Combinatorics 6, no. 3 (1985): 217–26. http://dx.doi.org/10.1016/s0195-6698(85)80031-7.

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24

Bandelt, Hans-Jürgen, Victor Chepoi, Andreas Dress, and Jack Koolen. "Combinatorics of lopsided sets." European Journal of Combinatorics 27, no. 5 (2006): 669–89. http://dx.doi.org/10.1016/j.ejc.2005.03.001.

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25

van Dam, Edwin R., and Willem H. Haemers. "Geometric and algebraic combinatorics." European Journal of Combinatorics 28, no. 7 (2007): 1877. http://dx.doi.org/10.1016/j.ejc.2006.08.001.

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26

Milutinović, Marija Jelić, Duško Jojić, Marinko Timotijević, Siniša T. Vrećica, and Rade T. Živaljević. "Combinatorics of unavoidable complexes." European Journal of Combinatorics 83 (January 2020): 103004. http://dx.doi.org/10.1016/j.ejc.2019.103004.

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27

Ardila, Federico, Graham Denham, and June Huh. "Lagrangian combinatorics of matroids." Algebraic Combinatorics 6, no. 2 (2023): 387–411. http://dx.doi.org/10.5802/alco.263.

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28

Curtis, Robert T., Kenneth H. Rosen, John G. Michaels, Jonathon L. Gross, Jerrold W. Grossman, and Douglas R. Shier. "Handbook of Discrete and Combinatorial Mathematics." Mathematical Gazette 84, no. 500 (2000): 364. http://dx.doi.org/10.2307/3621723.

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29

Hwang, Hsien-Kuei, Ralph Neininger, and Marek Zaionc. "Preface." Combinatorics, Probability and Computing 28, no. 4 (2019): 483–84. http://dx.doi.org/10.1017/s0963548319000166.

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This special issue is devoted to the Mathematical Analysis of Algorithms, which aims to predict the performance of fundamental algorithms and data structures in general use in Computer Science. The simplest measure of performance is the expected value of a cost function under natural models of randomness for the data, and finer properties of the cost distribution provide a deeper understanding of the complexity. Research in this area, which is intimately connected to combinatorics and random discrete structures, uses a rich variety of combinatorial, analytic and probabilistic methods.

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30

Jukna, Stasys. "Combinatorics of Monotone Computations." Combinatorica 19, no. 1 (1999): 65–85. http://dx.doi.org/10.1007/s004930050046.

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31

LENCZEWSKI, ROMUALD, and RAFAŁ SAŁAPATA. "DISCRETE INTERPOLATION BETWEEN MONOTONE PROBABILITY AND FREE PROBABILITY." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 01 (2006): 77–106. http://dx.doi.org/10.1142/s021902570600224x.

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We construct a sequence of states called m-monotone product states which give a discrete interpolation between the monotone product of states of Muraki in monotone probability and the free product of states of Avitzour and Voiculescu in free probability. We derive the associated basic limit theorems and develop the combinatorics based on non-crossing ordered partitions with monotone order starting from depth m. We deduce an explicit formula for the Cauchy transforms of the m-monotone central limit measures and for the associated Jacobi coefficients. A new type of combinatorics of inner blocks

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32

Mahajan, Ginika, Sanjay Tiwari, Rakesh Sharma, Rohit Kumar Gupta, and Pankaj Dadheech. "Discrete mathematics for strengthening multivariate polynomial cryptography by addressing vulnerabilities." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 7 (2024): 2123–32. http://dx.doi.org/10.47974/jdmsc-2085.

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Multivariate Polynomial Cryptography (MPC) has emerged as a promising candidate for securing digital communication in the post-quantum era. Despite its potential, existing MPC schemes exhibit vulnerabilities that compromise their effectiveness against both classical and quantum attacks. This paper leverages discrete mathematics to address these vulnerabilities, providing a robust mathematical foundation for enhancing the security and efficiency of MPC schemes. The paper begins by identifying critical weaknesses in current MPC algorithms, such as susceptibility to algebraic attacks and high com

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33

Anthony, Martin, Endre Boros, Peter L. Hammer, and Alexander Kogan. "Introduction to special volume of Discrete Applied Mathematics." Discrete Applied Mathematics 144, no. 1-2 (2004): 1. http://dx.doi.org/10.1016/j.dam.2004.06.004.

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34

von Bell, Matias, та Martha Yip. "Schröder combinatorics and ν-associahedra". European Journal of Combinatorics 98 (грудень 2021): 103415. http://dx.doi.org/10.1016/j.ejc.2021.103415.

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35

Kim, Dongsu, and Jiang Zeng. "Combinatorics of generalized Tchebycheff polynomials." European Journal of Combinatorics 24, no. 5 (2003): 499–509. http://dx.doi.org/10.1016/s0195-6698(03)00046-5.

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36

Guttmann, A. J. "On combinatorics and statistical mechanics." Annals of Combinatorics 3, no. 2-4 (1999): iii—iv. http://dx.doi.org/10.1007/bf01608778.

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37

Kaliszewski, Ryan, and Jennifer Morse. "Colorful combinatorics and Macdonald polynomials." European Journal of Combinatorics 81 (October 2019): 354–77. http://dx.doi.org/10.1016/j.ejc.2019.05.006.

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38

Jambu, Michel, and Luis Paris. "Combinatorics of inductively factored arrangements." European Journal of Combinatorics 16, no. 3 (1995): 267–92. http://dx.doi.org/10.1016/0195-6698(95)90032-2.

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39

Gropp, Harald. "Configurations between geometry and combinatorics." Discrete Applied Mathematics 138, no. 1-2 (2004): 79–88. http://dx.doi.org/10.1016/s0166-218x(03)00271-3.

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40

Albenque, Marie. "Bijective combinatorics of positive braids." Electronic Notes in Discrete Mathematics 29 (August 2007): 225–29. http://dx.doi.org/10.1016/j.endm.2007.07.038.

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41

Sebő, András, and Zoltán Szigeti. "Preface: Graph theory and combinatorics." Discrete Applied Mathematics 209 (August 2016): 1. http://dx.doi.org/10.1016/j.dam.2016.02.021.

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42

Khoshnoudirad, Daniel. "Farey lines defining Farey diagrams and application to some discrete structures." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 73–84. http://dx.doi.org/10.2298/aadm150219008k.

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The aim of the paper is to study some of the analytical properties of Farey diagrams of order (m,n), which are associated to the (m,n)-cubes, that is the pieces of discrete planes, occurring in discrete mathematics. We give a closed formula for the number of Farey lines defining Farey diagrams. This number asymptotically behaves as mn(m+n)=?(3). Then we establish the relation with some discrete structures in the field of discrete geometry in particular.

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43

Baylis, John, R. P. Grimaldi, and K. Kalmanson. "Discrete and Combinatorial Mathematics, an Applied Introduction." Mathematical Gazette 71, no. 455 (1987): 86. http://dx.doi.org/10.2307/3616325.

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44

Astalini, Astalini, Luis Roberto Pino-Fan, Somjai Boonsiri, U. L. Zainudeen, Tin Nwe Aye, and Vu Duong. "Development of Combinatorial Optimization Models with Discrete Mathematics Methods in Mathematical Physics Courses." Interval: Indonesian Journal of Mathematical Education 1, no. 2 (2023): 110–17. https://doi.org/10.37251/ijome.v1i2.1354.

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Purpose of the study: This research aims to develop a combinatorial optimization model based on discrete mathematical methods that can be applied to mathematical physics problems in complex systems, such as molecular energy configurations and viscoelastic system simulations. Methodology: The study used a development approach with ADDIE design (Analysis, Design, Development, Implementation, Evaluation). Data were obtained through interviews, simulations, and instrument validation involving lecturers and students of mathematical physics. Main Findings: The results of the study showed that the de

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45

Chandrasekaran, N., and N. Sridharan. "Discrete Fuzzy Matroids." Electronic Notes in Discrete Mathematics 15 (May 2003): 59. http://dx.doi.org/10.1016/s1571-0653(04)00530-x.

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46

Largeteau-Skapin, Gaëlle, and Eric Andres. "Discrete-Euclidean operations." Discrete Applied Mathematics 157, no. 3 (2009): 510–23. http://dx.doi.org/10.1016/j.dam.2008.05.034.

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47

Kuba, Attila, László Ruskó, Zoltán Kiss, and Antal Nagy. "Discrete Reconstruction Techniques." Electronic Notes in Discrete Mathematics 20 (July 2005): 385–98. http://dx.doi.org/10.1016/j.endm.2005.04.005.

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48

Gu, Nancy S. S., and Helmut Prodinger. "Combinatorics on lattice paths in strips." European Journal of Combinatorics 94 (May 2021): 103310. http://dx.doi.org/10.1016/j.ejc.2021.103310.

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49

Labelle, Jacques, and Yeong Nan Yeh. "Some Combinatorics of the Hypergeometric Series." European Journal of Combinatorics 9, no. 6 (1988): 593–605. http://dx.doi.org/10.1016/s0195-6698(88)80056-8.

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50

Sills, Andrew V. "The Combinatorics of MacMahon’s Partial Fractions." Annals of Combinatorics 23, no. 3-4 (2019): 1073–86. http://dx.doi.org/10.1007/s00026-019-00460-9.

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