Algebraic combinatorics

Summary

Algebraic combinatorics uses methods of abstract algebra to study combinatorial structures, and combinatorial methods to study algebraic objects, see the definition. Central topics are symmetric functions, Young tableaux and the representation theory of the symmetric group. Other topics are association schemes, incidence algebras of partially ordered sets, and the algebra of simplicial complexes. Many of its results are identities that have both an algebraic proof and a bijective proof.