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Everything about Combinatorics
Branch of discrete mathematics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: CombinatoricsA 5-minute orientation
- Skim a recent paper: Liquid Metal Combinatorics toward Materials DiscoveryInfluential work since 2022
- Pick up a classic book: Introduction to graph theoryThe most-reprinted book on the subject
- Read the landmark paper: Topological Classification of Crystalline Insulators through Band Structure CombinatoricsCited 662 times
- Go sideways: Discrete geometryA closely related topic
- Go sideways: Glossary of areas of mathematicsA closely related topic
📖 Definitions
Noun a branch of mathematics that studies (usually finite) collections of objects that satisfy specified criteria
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Topological Classification of Crystalline Insulators through Band Structure Combinatorics
Tilting theory and cluster combinatorics
Combinatorics of gauge fields
Combinatorics and topology of complements of hyperplanes
Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry a
Hook young diagrams with applications to combinatorics and to representations of Lie superalgebras
Portable Food‐Freshness Prediction Platform Based on Colorimetric Barcode Combinatorics and Deep Convolutional Neural Networks
Invariants of finite groups and their applications to combinatorics
🆕 Influential since 2022
Liquid Metal Combinatorics toward Materials Discovery
Liquid Metal Combinatorics toward Materials Discovery (Adv. Mater. 52/2023)
Polyhedral geometry and combinatorics of an autocatalytic ecosystem
Local problems on grids from the perspective of distributed algorithms, finitary factors, and descriptive combinatorics
Performance evaluation methodology for gas turbine power plants using graph theory and combinatorics
📚 Books worth reading
Introduction to graph theoryRobin J. Wilson · 1972
Introduction to modern cryptographyJonathan Katz, Yehuda Lindell · 2007
Graphs & digraphsGary Chartrand, L. Lesniak · 1986
Graph theory and its applicationsJonathan L. Gross, Jay Yellen · 1999
Applied combinatoricsAlan C. Tucker · 1980
Chromatic graph theoryGary Chartrand, Zhang, Ping · 2008
Mathematical proofsGary Chartrand, Albert D. Polimeni · 2002
Logic Colloquium 2005Logic Colloquium (2005 Athens, Greece), Costas Dimitracopoulos · 2007
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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