🧮 Combinatorics

Based on Applied Combinatorics by Keller & Trotter, licensed CC BY-SA.

The art of counting and structure. Compressed to runnable code, SVG diagrams, and plain English. Scheme first, Python in the fold.

	Chapter
1.	Counting Foundations	Sum and product rules, permutations, combinations: how many ways are there?	🧮
2.	Binomial Coefficients	Pascal's triangle, the binomial theorem, and the identities that fall out of choosing	🧮
3.	Bijective Proof	Counting one set two ways: the cleanest proofs in all of mathematics	🧮
4.	Inclusion–Exclusion	Counting when sets overlap, and the derangements it produces	🧮
5.	Generating Functions	Encode a whole sequence as one power series, then do algebra on it	🧮
6.	Recurrence Relations	Fibonacci, linear recurrences, and how to solve them in closed form	🧮
7.	Partially Ordered Sets	Chains, antichains, and the Dilworth/Mirsky duality that governs them	🧮
8.	Graph Theory	Trees, matchings, and coloring: combinatorics with edges	🧮
9.	Pólya Enumeration	Burnside's lemma and counting structures up to symmetry	🧮
10.	Probabilistic & Extremal Methods	Pigeonhole at scale, Ramsey, and the first-moment method: the adversarial frontier	🧮

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