Mathematics - Combinatorics

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Combinatorics Classifying Perfectness in Unitary Cayley Graphs

Examining properties of perfect unitary Cayley graphs related to finite rings.

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

2025-06-12T19:22:28+00:00 ― 6 min read

Latest Articles

Combinatorics Refining the Crossing Lemma in Graph Theory

New methods improve estimates of edge crossings in dense graphs.

Aaron Büngener, Michael Kaufmann

2025-06-12T12:49:13+00:00 ― 6 min read

Combinatorics Understanding Intersection Graphs and Their Applications

A look into intersection graphs and their significance in various fields.

Laura Merker, Lena Scherzer, Samuel Schneider

2025-06-12T12:23:00+00:00 ― 5 min read

Probability Understanding Record-Biased Permutations

This article examines unique arrangements of numbers focusing on records.

Mathilde Bouvel, Cyril Nicaud, Carine Pivoteau

2025-06-12T11:30:34+00:00 ― 4 min read

Logic Eulerian Paths: Infinite Graphs and Their Challenges

Examining the complexities of Eulerian paths in infinite graphs.

Nicanor Carrasco-Vargas, Valentino Delle Rose, Cristóbal Rojas

2025-06-12T09:19:29+00:00 ― 6 min read

Combinatorics Understanding BP Decompositions and Their Impact

A look at BP decompositions and their significance in mathematics.

Suho Oh, Edward Richmond

2025-06-12T08:53:16+00:00 ― 6 min read

Combinatorics Analyzing Crease Patterns in Paper Folding

A look at unique crease patterns formed by folding paper.

Johan Nilsson

2025-06-12T08:00:50+00:00 ― 5 min read

Combinatorics Cubic Graphs: Eigenvalues and Their Implications

A look into cubic graphs and their eigenvalue properties.

Krystal Guo, Gordon F. Royle

2025-06-12T05:23:32+00:00 ― 6 min read

Combinatorics Exploring Circular-Arc and Chordal Graphs

A look into the relationships and characteristics of circular-arc and chordal graphs.

Yixin Cao, Tomasz Krawczyk

2025-06-12T00:08:56+00:00 ― 5 min read

Combinatorics Understanding Power Graphs and Oriented Diameters

An overview of power graphs, their orientations, and implications in group theory.

Deepu Benson, Bireswar Das, Dipan Dey

2025-06-11T21:31:38+00:00 ― 3 min read

Combinatorics A Closer Look at Infinite Lotteries

Explore how infinite lotteries work and their intriguing outcomes.

Enciso-Alva, Julio Cesar

2025-06-11T19:20:33+00:00 ― 6 min read

Group Theory An Insight Into Weakly Systolic Complexes

Discover the unique properties of weakly systolic complexes in geometry and topology.

Ioana-Claudia Lazar

2025-06-11T18:01:54+00:00 ― 5 min read

Combinatorics Matroids: A Comprehensive Overview

Discover the fundamental concepts and applications of matroids in mathematics.

Franquiz Caraballo Alba, Jeffery Liu

2025-06-11T17:35:41+00:00 ― 5 min read

Combinatorics Understanding Generalized Paley Graphs

An overview of the structure and properties of generalized Paley graphs.

Vincent Bonini, Daniel Chamberlin, Stephen Cook

2025-06-11T16:43:15+00:00 ― 5 min read

Combinatorics Understanding Graph Theory's Chromatic Number

Exploring the relationship between chromatic number and minimum degree in graphs.

Zilong Yan, Yuejian Peng, Xiaoli Yuan

2025-06-11T12:21:05+00:00 ― 5 min read

Combinatorics The Role of Graph Theory in Chemistry

Examining how graph properties impact chemical compounds and their behaviors.

Swathi Shetty, B. R. Rakshith, Sayinath Udupa N.

2025-06-11T10:10:00+00:00 ― 5 min read

Combinatorics Examining Critical Groups and Graph Covers

This article explores the connections between critical groups and harmonic covers in graphs.

Mariia Vetluzhskikh, Dmitry Zakharov

2025-06-11T04:02:58+00:00 ― 4 min read

Probability Asymptotic Behavior of Symmetric Polynomials

Investigating the limits of symmetric polynomials as variables increase.

Alice Guionnet, Jiaoyang Huang

2025-06-11T03:36:45+00:00 ― 5 min read

Operator Algebras Measuring Noncommutative Distances in Graphs

Exploring novel measurements of distance in graphs using advanced mathematics and linear algebra.

Pierre Clare, Chi-Kwong Li, Edward Poon

2025-06-10T23:14:35+00:00 ― 5 min read

Discrete Mathematics Optimizing Refueling Station Placement in Electric Vehicle Networks

Learn how digraphs improve refueling station placement for electric vehicles.

Lukas Dijkstra, Andrei Gagarin, Padraig Corcoran

2025-06-10T18:26:12+00:00 ― 6 min read

Combinatorics Cluster Algebras and Punctured Surfaces

Exploring the intersection of cluster algebras and geometric surfaces with punctures.

Esther Banaian, Wonwoo Kang, Elizabeth Kelley

2025-06-10T16:41:20+00:00 ― 5 min read

Algebraic Geometry Understanding Anti-Symmetric Matrices and Determinants

A look into the role of anti-symmetric matrices in linear algebra.

Jacques Distler, Nathan Donagi, Ron Donagi

2025-06-10T16:39:30+00:00 ― 6 min read

Combinatorics Investigating Toric Posets in Mathematics

Toric posets offer new insights into the study of partially ordered sets.

Elise Catania

2025-06-10T15:22:41+00:00 ― 5 min read

Algebraic Geometry An Overview of Schubert and Spherical Varieties

Learn about important types of varieties in algebraic geometry.

Mahir Bilen Can, S. Senthamarai Kannan, Pinakinath Saha

2025-06-10T14:56:28+00:00 ― 4 min read

Machine Learning Understanding Sparse Graphs Through Their Line Graphs

A look at how sparse graphs relate to their line graphs and properties.

Sevvandi Kandanaarachchi, Cheng Soon Ong

2025-06-10T11:29:08+00:00 ― 5 min read

Artificial Intelligence Efficient Solutions for Column Permutation Problems

Learn how new methods improve column arrangement in binary matrices.

Júnior R. Lima, Viníicius Gandra M. Santos, Marco Antonio M. Carvalho

2025-06-10T10:08:05+00:00 ― 5 min read

Combinatorics Efficient Graph Representation with Adjacency Labeling Schemes

Learn how adjacency labeling optimizes graph data storage and analysis.

Édouard Bonnet, Julien Duron, John Sylvester

2025-06-10T09:15:39+00:00 ― 6 min read

Discrete Mathematics Understanding Fault Tolerant Metric Dimension in Bicyclic Graphs

A look at how graphs help in real-world applications like logistics.

Tauseef Asif, Ghulam Haidar, Faisal Yousafzai

2025-06-09T17:58:04+00:00 ― 5 min read

Combinatorics Understanding Joint Embedding Property in Graphs

An overview of joint embedding property and its implications for cographs and trees.

Daniel Carter

2025-06-09T17:31:51+00:00 ― 5 min read

Combinatorics Insights into Planar -Complete Graphs

This study reveals the limits and structures of planar -complete graphs.

Susobhan Bandopadhyay, Sagnik Sen, S Taruni

2025-06-09T15:20:46+00:00 ― 5 min read

Combinatorics Diving into Positive Semi-Definite Matrices

Exploring the properties and implications of positive semi-definite matrices in mathematics.

Robert Angarone, Daniel Soskin

2025-06-09T11:24:49+00:00 ― 5 min read

Combinatorics The Relationship Between Graphs and Trees

Exploring how trees fit into graphs through connections and structures.

Paul Bastide, Clément Legrand-Duchesne, Alp Müyesser

2025-06-09T10:06:10+00:00 ― 5 min read

Commutative Algebra Affine Semigroups and Their Applications

A look into affine semigroups and their special types.

J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio

2025-06-09T08:21:18+00:00 ― 4 min read

Computational Complexity Advancements in Communication Complexity of Group Multiplication

Research reveals new insights into group multiplication and its communication complexity.

Harm Derksen, Chin Ho Lee, Emanuele Viola

2025-06-09T07:02:39+00:00 ― 6 min read

Number Theory The Role of Additive Bases in Number Theory

Exploring how additive bases help express numbers as sums from specific sets.

Boris Bukh, Peter van Hintum, Peter Keevash

2025-06-09T02:14:16+00:00 ― 4 min read

Combinatorics Understanding the Sombor Index and Its Impact

Explore the Sombor index and its relevance in graph theory and chemistry.

Maryam Mohammadi, Hasan Barzegar

2025-06-08T21:52:06+00:00 ― 5 min read

Optimization and Control Advancing Defender-Attacker Problem Models

New methods improve strategies for defending systems against attacks.

Samuel Affar, Hugh Medal

2025-06-08T14:00:12+00:00 ― 6 min read

Probability The Dynamics of the Bernoulli-Laplace Urn Model

A study of random mixing processes using two urns of colored balls.

Sam Olesker-Taylor, Dominik Schmid

2025-06-08T08:19:23+00:00 ― 6 min read

Combinatorics Understanding Automata Networks and Their Dynamics

Exploring the structure and behavior of automata networks in various fields.

Florian Bridoux, Aymeric Picard Marchetto, Adrien Richard

2025-06-08T05:15:52+00:00 ― 5 min read

Combinatorics Transforming Spanning Trees through Matroid Theory

This study examines the process of reconfiguring spanning trees using matroid concepts.

Tesshu Hanaka, Yuni Iwamasa, Yasuaki Kobayashi

2025-06-08T04:49:39+00:00 ― 6 min read

Combinatorics Understanding Co-Degree in Hypergraphs

Exploring co-degree and its significance in hypergraph structures.

Anastasia Halfpap, Van Magnan

2025-06-08T03:31:00+00:00 ― 6 min read