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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
semanticscholar +4 more sources
Symplectic rigidity and quantum mechanics [PDF]
, 2018 Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline similarities and differences to other combinatorial Hodge theories.
Guichard, Olivier, Wienhard, Anna
openaire +19 more sources
Journal of Combinatorial Designs, EarlyView.ABSTRACT We investigate the lazy burning process for Latin squares by studying their associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is initially burned, and that burning spreads to neighboring vertices over time via a specified propagation rule.
Anthony Bonato +3 more
wiley +1 more source
Conformal Hypergraphs: Duality and Implications for the Upper Clique Transversal Problem
Journal of Graph Theory, EarlyView.ABSTRACT Given a hypergraph H ${\rm{ {\mathcal H} }}$, the dual hypergraph of H ${\rm{ {\mathcal H} }}$ is the hypergraph of all minimal transversals of H ${\rm{ {\mathcal H} }}$. The dual hypergraph is always Sperner, that is, no hyperedge contains another.
Endre Boros +3 more
wiley +1 more source
Weighted Turán Theorems With Applications to Ramsey‐Turán Type of Problems
Journal of Graph Theory, EarlyView.ABSTRACT We study extensions of Turán Theorem in edge‐weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey‐Turán type problems.
József Balogh +2 more
wiley +1 more source
Abundant Neighborhoods, Two‐Sided Markets, and Maximal Matchings
Naval Research Logistics (NRL), EarlyView.ABSTRACT I introduce a new graph‐theoretic property called abundant neighborhoods. This property is motivated by studying the thickness of economic markets. A vertex is, roughly, guaranteed to match if and only if it has an abundant neighborhood.
Muhammad Maaz
wiley +1 more source
Combinatorial optimization approach for the efficient reuse of RC components
Structural Concrete, EarlyView.Abstract The reuse of reinforced concrete (RC) components from deconstructed buildings offers a promising approach to reduce the environmental impact of new constructions. However, it represents a complex combinatorial optimization problem to efficiently place the available modules, which vary in geometry and load‐bearing capacity, into new structures ...
Jannis Rose +4 more
wiley +1 more source
Isosurface Extraction for Signed Distance Functions using Power Diagrams
Computer Graphics Forum, EarlyView.Abstract Contouring an implicit function typically considers function values in the vicinity of the desired level set, only. In a recent string of works, Sellán at al. have demonstrated that signed distance values contain useful information also if they are further away from the surface.
M. Kohlbrenner, M. Alexa
wiley +1 more source
On the isomorphism problem for monoids of product‐one sequences
Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1482-1495, May 2025.Abstract Let G1$G_1$ and G2$G_2$ be torsion groups. We prove that the monoids of product‐one sequences over G1$G_1$ and over G2$G_2$ are isomorphic if and only if the groups G1$G_1$ and G2$G_2$ are isomorphic. This was known before for abelian groups.
Alfred Geroldinger, Jun Seok Oh
wiley +1 more source
Coloured shuffle compatibility, Hadamard products, and ask zeta functions
Bulletin of the London Mathematical Society, EarlyView.Abstract We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so‐called ask zeta functions of direct sums of modules of matrices or class‐ and orbit‐counting zeta functions of direct products of nilpotent groups.
Angela Carnevale +2 more
wiley +1 more source