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Advances in Discrete Mathematics: From Combinatorics to Cryptography
Discrete mathematics forms the foundation for various fields, including computer science and cryptography, by providing essential tools for problem-solving in discrete structures.
Romi Bala, Hemant Pandey
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Contributions by Aart Blokhuis to finite geometry, discrete mathematics, and combinatorics [PDF]
Simeon Ball+2 more
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A Discrete Mathematics Approach for Understanding Risk Factors in Overactive Bladder Treatment. [PDF]
Introduction Discrete mathematics, a branch of mathematics that includes graph theory, combinatorics, and logic, focuses on discrete mathematical structures.
Okui N.
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Notes on Equitable Partitions into Matching Forests in Mixed Graphs and into $b$-branchings in Digraphs [PDF]
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]
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]
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]
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]
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]
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]
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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