Algebraic Combinatorics¶

8 domain-specific abstractions whose origin domain is Algebraic Combinatorics.

Incidence algebra — An algebra of interval-indexed functions on a locally finite partially ordered set, with multiplication given by convolution over intermediate elements.
Order polynomial — The polynomial whose value at n counts order-preserving maps from a finite poset to an n-element chain.
Order polytope — The convex polytope of order-preserving maps from a finite poset into the unit interval.
Quasisymmetric function — A bounded-degree formal power series whose coefficient depends on an exponent composition but not on the particular increasing sequence of variable indices.
Representation theory of the symmetric group — The classification and analysis of symmetric-group actions on vector spaces through partitions, Young diagrams, tableaux, characters and Specht modules.
Robinson–Schensted–Knuth correspondence — A weight-preserving bijection between nonnegative-integer matrices and pairs of semistandard Young tableaux of equal shape.
Spherical Design — A finite equal-weight point set on a unit sphere whose discrete average exactly matches the sphere average for every polynomial through a declared degree.
Stanley symmetric function — A symmetric function indexed by a permutation and generated from its reduced words, encoding reduced-decomposition and Schubert-polynomial combinatorics.