Mathematics - Combinatorics

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Spectral Theory The Secrets of Regular Graphs Revealed

Uncovering the intriguing eigenvalues and spectral edges of regular graphs.

Dingding Dong, Theo McKenzie

2025-03-12T18:38:30+00:00 ― 6 min read

Latest Articles

Combinatorics The Intricacies of Higher Bruhat Orders

Explore a fascinating area of mathematics connecting sets and relationships.

Herman Chau

2025-03-09T13:23:20+00:00 ― 6 min read

Combinatorics The Intricacies of Trees and T-Fractions

Discover how trees and T-fractions reveal complex mathematical relationships.

Veronica Bitonti, Bishal Deb, Alan D. Sokal

2025-03-09T00:04:10+00:00 ― 6 min read

Combinatorics Balancing Connections: The Zarankiewicz Challenge

A look into the Unbalanced Zarankiewicz problem in graph theory.

Lili Ködmön, Anqi Li, Ji Zeng

2025-03-08T21:24:20+00:00 ― 6 min read

Combinatorics The Fascinating World of Quasi-Orthogonal Matrices

Discover the intriguing properties and applications of quasi-orthogonal matrices.

Abderrahim Boussaïri, Brahim Chergui, Zaineb Sarir

2025-03-08T18:44:30+00:00 ― 5 min read

Combinatorics The Dance of Graph Theory and Stability

Exploring how dance parties reflect stable sets in graph theory.

Koji Matsushita, Akiyoshi Tsuchiya

2025-03-08T16:04:40+00:00 ― 6 min read

Combinatorics The Symmetry of Mathematical Functions

Discover the magic of symmetric functions and their connections.

Aritra Bhattacharya

2025-03-08T13:24:50+00:00 ― 6 min read

Optimization and Control New Method Boosts Solving of MWIS Problem

A fresh approach enhances efficiency in tackling Maximum Weight Independent Set challenges.

Ernestine Großmann, Kenneth Langedal, Christian Schulz

2025-03-07T18:46:00+00:00 ― 5 min read

Combinatorics The Colorful World of Quasisymmetric Functions

Discover the impact of colors on quasisymmetric functions in mathematics.

Spencer Daugherty

2025-03-07T10:46:30+00:00 ― 7 min read

Combinatorics Connecting Dots: The Magic of Chebyshev Polynomials and Fan Graphs

Discover how Chebyshev polynomials and fan graphs reveal hidden connections in math.

Wojciech Młotkowski, Nobuaki Obata

2025-03-06T10:48:00+00:00 ― 6 min read

Combinatorics The Intriguing World of Finite Groups

Discover how small doubling sets affect Fourier coefficients in mathematics.

Ilya D. Shkredov

2025-03-05T10:49:30+00:00 ― 5 min read

Combinatorics Counting Diagonalizable Matrices in Finite Fields

Discover how to count diagonalizable matrices using finite fields and graph theory.

Catherine Falvey, Heewon Hah, William Sheppard

2025-03-05T08:09:40+00:00 ― 6 min read

Logic The Importance of Regularity Lemmas in Mathematics

Discover how regularity lemmas simplify complex structures in mathematics.

Anand Pillay, Atticus Stonestrom

2025-03-04T05:31:20+00:00 ― 6 min read

Combinatorics The Mystery of Unit-Distance Graphs

Discover the quest to maximize connections in unit-distance graphs.

Boris Alexeev, Dustin G. Mixon, Hans Parshall

2025-03-01T18:55:00+00:00 ― 5 min read

Combinatorics The Quest to Maximize Set Systems

Researchers tackle the complexity of set systems and VC-dimension limits.

Gennian Ge, Zixiang Xu, Chi Hoi Yip

2025-03-01T16:15:10+00:00 ― 6 min read

Combinatorics The Intriguing World of Random Graphs

Discover how random graphs shape our understanding of connections and rigidity.

Yuval Peled, Niv Peleg

2025-02-26T21:39:20+00:00 ― 7 min read

Combinatorics Spreading Secrets: The Art of Graph Burning

Discover how information spreads through networks using graph burning techniques.

Danielle Cox, M. E. Messinger, Kerry Ojakian

2025-02-26T11:00:00+00:00 ― 6 min read

Algebraic Geometry Curves and Varieties: The Beauty of Geometry

Exploring rational normal curves and the ABCT variety in mathematics.

Daniele Agostini, Lakshmi Ramesh, Dawei Shen

2025-02-26T01:45:38+00:00 ― 8 min read

Algebraic Geometry Exploring the Depths of Moduli Spaces

A glimpse into the fascinating worlds of curves and their structures.

Siddarth Kannan, Terry Dekun Song

2025-02-26T00:10:06+00:00 ― 7 min read

Combinatorics The Fascinating World of Self-Avoiding Polygons

Discover the intriguing patterns of self-avoiding polygons on lattice grids.

Jean Fromentin, Pierre-Louis Giscard, Yohan Hosten

2025-02-25T16:21:10+00:00 ― 8 min read

Combinatorics Unraveling the World of Directed Graphs

Discover the fascinating structures of rooted arborescences and covering graphs.

Muchen Ju, Junjie Ni, Kaixin Wang

2025-02-25T13:41:20+00:00 ― 5 min read

Data Structures and Algorithms Dynamic Graphs: Balancing Stability and Approximation

A deep dive into dynamic graphs and algorithms for managing sets.

Mark de Berg, Arpan Sadhukhan, Frits Spieksma

2025-02-25T03:02:00+00:00 ― 6 min read

Probability The Exciting World of Random Walks

Discover how random walks work in graphs and their real-life applications.

Sam Olesker-Taylor, Thomas Sauerwald, John Sylvester

2025-02-25T00:22:10+00:00 ― 6 min read

Combinatorics Exploring the World of Q-Matroids

A look into the fascinating structures of q-matroids and their properties.

Gianira N. Alfarano, Eimear Byrne, Andrew Fulcher

2025-02-24T16:22:40+00:00 ― 6 min read

Discrete Mathematics Mastering Mixed Linear Layouts in Graphs

Learn how to organize graph connections using stacks, queues, and thick patterns.

Deborah Haun, Laura Merker, Sergey Pupyrev

2025-02-24T03:03:30+00:00 ― 4 min read

Analysis of PDEs Connecting Kinetic and Graph Theories

Exploring the links between particle behavior and network relationships.

Datong Zhou

2025-02-23T16:24:10+00:00 ― 6 min read

Combinatorics The Secrets of Graph Rigidity Uncovered

Discover the fascinating world of graph rigidity and its implications.

Michael Krivelevich, Alan Lew, Peleg Michaeli

2025-02-23T08:24:40+00:00 ― 7 min read

Combinatorics Discovering Growth Bijections in Math

Explore the relationships between structures through growth bijections and their fascinating applications.

Jérémie Bettinelli, Éric Fusy, Baptiste Louf

2025-02-22T21:45:20+00:00 ― 5 min read

Number Theory The Fascinating World of 4-Dimensional Polytopes

Discover the intriguing shapes beyond our 3-dimensional space.

Anji Dong, The Nguyen, Alexandru Zaharescu

2025-02-22T13:45:50+00:00 ― 6 min read

Machine Learning The Rise of Group Equivariant Neural Networks

Discover how these networks transform data handling with symmetries.

Edward Pearce-Crump, William J. Knottenbelt

2025-02-22T02:30:48+00:00 ― 6 min read

Combinatorics Rank-Metric Codes: Safeguarding Data Transmission

Learn how rank-metric codes protect your messages from errors.

Giuseppe Cotardo, Alberto Ravagnani, Ferdinando Zullo

2025-02-20T08:29:10+00:00 ― 5 min read

Combinatorics Cleaning Up Graphs: Patterns and Strategies

Learn how mathematicians tackle patterns in graphs effectively.

V. Gladkova

2025-02-19T03:11:00+00:00 ― 7 min read

Combinatorics The Fascinating World of Hypergraphs

Explore the unique properties and dynamics of hypergraphs and random processes.

Felix Joos, Marcus Kühn

2025-02-18T19:11:30+00:00 ― 4 min read

Combinatorics Crystals in Mathematics: A Deep Dive

Discover the fascinating world of mathematical crystals and their role in Lie algebras.

Álvaro Gutiérrez

2025-02-18T08:32:10+00:00 ― 8 min read

Combinatorics Counting the Irregular: A Journey into Irrational Combinatorics

Discover how irrational numbers play a role in combinatorial challenges.

David Bevan, Julien Condé

2025-02-16T13:54:50+00:00 ― 6 min read

Algebraic Geometry Exploring the Intricacies of Log-Surfaces

A deep dive into the fascinating world of log-surfaces and their complexities.

Bartosz Naskręcki, Piotr Pokora

2025-02-16T11:15:00+00:00 ― 7 min read

Mathematical Physics The Dance of Particles: A Physics Perspective

Explore how identical particles interact and scatter in a line arrangement.

Denis Bashkirov

2025-02-16T06:06:42+00:00 ― 6 min read

Combinatorics The Colorful World of Rainbow Arborescences

Discover the intriguing Rainbow Arborescence Conjecture in graph theory.

Kristóf Bérczi, Tamás Király, Yutaro Yamaguchi

2025-02-16T00:35:40+00:00 ― 4 min read

Combinatorics Uncovering Independent Sets in Hypergraphs

New methods enhance our grasp of independent sets in hypergraphs.

Patrick Arras, Frederik Garbe, Felix Joos

2025-02-15T11:16:30+00:00 ― 8 min read

Data Structures and Algorithms Unraveling Sparse Induced Subgraphs

Discover the complexities and applications of sparse induced subgraphs in graph theory.

Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk

2025-02-15T08:36:40+00:00 ― 6 min read

Combinatorics The Importance of Interval-Closed Sets in Mathematics

Discover the role of interval-closed sets in organizing complex systems.

Sergi Elizalde, Nadia Lafrenière, Joel Brewster Lewis

2025-02-14T16:37:40+00:00 ― 6 min read

Number Theory The Secrets Behind Binary Numbers Revealed

Discover the hidden complexity of binary numbers and their applications in technology.

Bartosz Sobolewski

2025-02-13T03:20:00+00:00 ― 5 min read

Algebraic Geometry Unraveling the Mysteries of Trigonal Curves

Discover the fascinating world of trigonal curves in algebraic geometry.

V. I. Zvonilov

2025-02-12T22:00:20+00:00 ― 7 min read

Representation Theory Understanding Weight Multiplicities in Lie Algebras

A deep dive into weight multiplicities and their role in Lie algebras.

Portia X. Anderson, Esther Banaian, Melanie J. Ferreri

2025-02-11T08:42:40+00:00 ― 5 min read

Combinatorics The Colorful World of Ramsey Numbers

Discover the challenge of Ramsey numbers in coloring and connections.

Pavel Pudlák, Vojtěch Rödl

2025-02-11T00:43:10+00:00 ― 5 min read

Combinatorics The Hidden World of Totally Positive Skew-Symmetric Matrices

Discover the unique properties and applications of totally positive skew-symmetric matrices.

Jonathan Boretsky, Veronica Calvo Cortes, Yassine El Maazouz

2025-02-09T11:25:30+00:00 ― 6 min read

Combinatorics The Art and Science of Packing

Discover the fascinating world of packing shapes and strategies in mathematics.

A. D. Kislovskiy, E. Yu. Lerner, I. A. Senkevich

2025-02-09T03:26:00+00:00 ― 6 min read

Combinatorics The Art of Lattice Triangulations

Discover the fascinating world of lattice triangulations in mathematics.

Stepan Orevkov

2025-02-08T19:26:30+00:00 ― 6 min read

Data Structures and Algorithms The Challenge of the Sparsest Cut

A deep dive into the sparsest cut problem and its significance in various fields.

Tommaso d'Orsi, Chris Jones, Jake Ruotolo

2025-02-08T03:27:30+00:00 ― 7 min read

Computational Geometry The Fascinating World of Space-Filling Curves

Discover how space-filling curves uniquely cover every point in a space.

Zuguang Gu

2025-02-07T03:29:00+00:00 ― 5 min read

Combinatorics The Colorful World of Permutations

Discover the vibrant structures of permutations and Young tableaux in combinatorics.

Martha Du Preez, William Q. Erickson, Jonathan Feigert

2025-02-06T19:29:30+00:00 ― 5 min read

Combinatorics Connecting the Dots: The Chen-Raspaud Conjecture

Discover how graphs connect and the implications of the Chen-Raspaud conjecture.

Michał Fiedorowicz

2025-02-06T06:10:20+00:00 ― 6 min read

Combinatorics Building Better Networks on a Budget

Learn how to connect people effectively without overspending.

Daniel Iľkovič, Jared León, Xichao Shu

2025-02-05T22:10:50+00:00 ― 7 min read

Combinatorics The Hidden Math in Paper Folding

Discover how paper folding reveals fascinating mathematical patterns and properties.

Jeffrey Shallit

2025-02-04T19:32:30+00:00 ― 5 min read

Combinatorics Finding Balance in Strategic Choices

Explore how players navigate decisions in games and everyday life.

Claus Hertling, Matija Vujic

2025-02-04T16:52:40+00:00 ― 6 min read

Analysis of PDEs Efficient Data Clustering with Volume Constraints

Discover how the volume-constrained MBO scheme improves data organization and analysis.

Fabius Krämer, Tim Laux

2025-02-04T06:13:20+00:00 ― 5 min read

Combinatorics The Strategic Battle of Graph Coloring

Alice and Bob face off in a challenging coloring game.

Caroline Brosse, Nicolas Martins, Nicolas Nisse

2025-02-04T03:33:30+00:00 ― 6 min read

Data Structures and Algorithms Minimizers: Bringing Order to Genetic Data Chaos

Learn how minimizers help make sense of vast genetic information.

Florian Ingels, Camille Marchet, Mikaël Salson

2025-02-03T19:34:00+00:00 ― 5 min read

Combinatorics The Mystery of Union-Closed Set Families

Exploring the conjecture around union-closed families of sets and their hidden elements.

Cory H. Colbert

2025-02-03T06:14:50+00:00 ― 6 min read

Combinatorics Understanding Partial Orders: A Friendly Approach

Learn how to organize friends using partial orders and their unique characteristics.

Iian B. Smythe, Mithuna Threz, Max Wiebe

2025-02-03T03:35:00+00:00 ― 7 min read

Combinatorics The Fascinating World of 1-Planar Graphs

Explore the intriguing nature and applications of 1-planar graphs.

Saman Bazargani, Therese Biedl, Prosenjit Bose

2025-02-01T03:38:00+00:00 ― 6 min read

Combinatorics The Enigmatic World of Thue-Morse Words

Discover the unique features and applications of Thue-Morse words in math and beyond.

M. Golafshan, M. Rigo, M. Whiteland

2025-01-31T19:38:30+00:00 ― 4 min read

Combinatorics The Intrigue of Off-Diagonal Ramsey Numbers

Dive into the fascinating world of off-diagonal Ramsey numbers in graph theory.

Sammy Luo, Zixuan Xu

2025-01-31T11:39:00+00:00 ― 5 min read

Combinatorics Connecting the Dots: The World of Graphs

Explore the fascinating connections and rules of graphs and Turán problems in this engaging article.

Xiamiao Zhao, Mei Lu

2025-01-30T22:19:50+00:00 ― 5 min read

Combinatorics The Intricacies of the Izergin-Korepin 19-Vertex Model

A deep dive into the world of complex particle systems.

Alexandr Garbali, Weiying Guo, Michael Wheeler

2025-01-30T15:15:36+00:00 ― 5 min read

Combinatorics The Hidden World of Hurwitz Numbers

Discover the fascinating role of Hurwitz numbers in math and science.

Nitin Kumar Chidambaram, Maciej Dołęga, Kento Osuga

2025-01-30T12:52:18+00:00 ― 4 min read

Probability Decoding Random Graphs: A Closer Look

Discover the intriguing world of random graphs and their real-life applications.

Xiangyi Zhu, Yizhe Zhu

2025-01-30T06:20:50+00:00 ― 5 min read

Combinatorics Cycle Convexity: A Deep Dive into Graphs

Explore cycle convexity in graphs and its real-world applications.

Bijo S. Anand, Ullas Chandran S. V., Julliano R. Nascimento

2025-01-30T03:41:00+00:00 ― 5 min read

Combinatorics The Magic of Continued Fractions

Discover how continued fractions simplify numbers and enhance calculations.

Michael J. Collins

2025-01-28T09:03:40+00:00 ― 5 min read

Combinatorics The Hidden Patterns of Tree Tiling in Graphs

Discover the intriguing structures of tree tiling in random graphs.

Sahar Diskin, Ilay Hoshen, Maksim Zhukovskii

2025-01-27T17:04:40+00:00 ― 6 min read

Combinatorics The Art of Recoloring Graphs

Discover the fascinating process of recoloring vertices in graph theory.

Stijn Cambie, Wouter Cames van Batenburg, Daniel W. Cranston

2025-01-27T09:05:10+00:00 ― 5 min read

Combinatorics Breaking Down Integer Partitions: The Math Behind Slices

Discover how integer partitions work and their significance in mathematics.

Taichiro Takagi

2025-01-26T09:06:40+00:00 ― 6 min read

Combinatorics Graphs and Tensors: Mapping Connections

Explore how graphs and tensors reveal relationships in data.

Chunmeng Liu, Changjiang Bu

2025-01-26T06:26:50+00:00 ― 6 min read

Combinatorics The Intricate World of Tight Trees and Ramsey Numbers

Uncovering the connections in math's tight trees and Ramsey numbers.

Jiaxi Nie

2025-01-26T03:47:00+00:00 ― 6 min read

Combinatorics Understanding Graph Functionality: Connections That Matter

Explore how graph functionality impacts relationships and interactions in various fields.

John Sylvester, Viktor Zamaraev, Maksim Zhukovskii

2025-01-25T17:07:40+00:00 ― 5 min read

Probability The Wild World of Bernoulli Excursions

Discover the fascinating patterns in random paths and their connections.

Vladislav Kargin

2025-01-25T03:48:30+00:00 ― 8 min read

High Energy Physics - Theory The Colorful World of Brane Tilings

Explore brane tilings and their fascinating role in physics.

Yang-Hui He, Vishnu Jejjala, Tomás S. R. Silva

2025-01-25T01:30:48+00:00 ― 6 min read

Combinatorics Seymour's Conjecture: The Search for Connections

Mathematicians investigate a challenging conjecture about directed graphs and their connections.

Hao Huang, Fei Peng

2025-01-24T19:49:00+00:00 ― 6 min read

Combinatorics The Strength of Graphs in Connectivity

Discover how strong graphs maintain connections in various fields.

Pablo Romero

2025-01-23T01:11:40+00:00 ― 6 min read

Combinatorics The Quest for Uniformly Most Reliable Graphs

Exploring how graphs maintain connections and find reliability in networks.

Pablo Romero

2025-01-22T22:31:50+00:00 ― 7 min read

Combinatorics Curvature in Trees: A Mathematical Perspective

Discover the role of curvature in understanding tree structures and their applications.

Sawyer Jack Robertson

2025-01-22T17:12:10+00:00 ― 8 min read