Domain 08 · Mathematics Codex
Discrete Mathematics & Combinatorics
The mathematics of finite and countable structures — graphs, combinations, codes, and algorithms.
Scope
Graph theory, combinatorics, enumerative combinatorics, Ramsey theory, coding theory, cryptography foundations, discrete geometry, algorithms and complexity.
Every algorithm runs on discrete structures. Every network is a graph. Every barcode is a code from coding theory. Ramanujan's work on partitions — a combinatorics problem — generated results that Atle Selberg and Paul Erdős described as among the most beautiful in mathematics. The Four Colour Theorem, proved in 1976 using a computer for the first time in mathematical history, lives in this domain.
Entries in this domain
Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
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Graph
Pending
A set of vertices connected by edges — the abstract structure underlying networks, maps, molecular bonds, and social connections.
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Combinatorics
Pending
The branch of mathematics studying how to count, arrange, and select from finite collections — traceable to Pingala's Chandaḥśāstra (c. 3rd century BCE, India).