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Advances in Discrete Mathematics: From Combinatorics to Cryptography
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2019 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.
Romi Bala, Hemant Pandey
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Contributions by Aart Blokhuis to finite geometry, discrete mathematics, and combinatorics [PDF]
Designs, Codes and Cryptography, 2022 Simeon Ball +2 more
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Quasirandomness in discrete mathematics, additive combinatorics and group theory
, 2020 The main objective of this bachelor's thesis will be to present the concept of quasirandomness in various mathematical contexts while proving all the pertinent results. We will introduce the results of Fan Chung and Ronald Graham on quasirandom graphs and quasirandom sets, and the results of Timothy Gowers on quasirandom groups.
Adrián Hernández Ramos
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Notes on Equitable Partitions into Matching Forests in Mixed Graphs and into $b$-branchings in Digraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 An equitable partition into branchings in a digraph is a partition of the arc set into branchings such that the sizes of any two branchings differ at most by one.
Kenjiro Takazawa
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Destroying Multicolored Paths and Cycles in Edge-Colored Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 We study the computational complexity of $c$-Colored $P_\ell$ Deletion and $c$-Colored $C_\ell$ Deletion. In these problems, one is given a $c$-edge-colored graph and wants to destroy all induced $c$-colored paths or cycles, respectively, on $\ell ...
Nils Jakob Eckstein +3 more
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Destroying Bicolored $P_3$s by Deleting Few Edges [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 We introduce and study the Bicolored $P_3$ Deletion problem defined as follows. The input is a graph $G=(V,E)$ where the edge set $E$ is partitioned into a set $E_r$ of red edges and a set $E_b$ of blue edges.
Niels Grüttemeier +3 more
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Pseudoperiodic Words and a Question of Shevelev [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner ...
Joseph Meleshko +3 more
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Antisquares and Critical Exponents [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $\textit{antisquare}$ is a nonempty word of the form $x\, \overline{x}$.
Aseem Baranwal +5 more
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Automatic sequences: from rational bases to trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system.
Michel Rigo, Manon Stipulanti
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On the VC-dimension of half-spaces with respect to convex sets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A family S of convex sets in the plane defines a hypergraph H = (S, E) as follows. Every subfamily S' of S defines a hyperedge of H if and only if there exists a halfspace h that fully contains S' , and no other set of S is fully contained in h.
Nicolas Grelier +3 more
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