Room 326

Abacus Proofs of Schur Function Identities (Following Nicholas A. Loehr)

Amritanshu Prasad

IMSc

In combinatorics, and Abacus is a specific type of sequence of labelled beads. Formulas involving Schur polynomials are proved by regarding them as encoding bead motions in an abacus.

Abaci can be used to prove Pieri's rule and its analogues for complete and power-sum symmetric functions, the equivalence of Cauchy's and Kostka's definitions of Schur functions, the Littlewood-Richardson rule for multiplying Schur functions, and a combinatorial interpretation of the inverse Kostka matrix.

This talk will be based on the article "Abacus Proofs of Schur Function Identities" by Nicholas A. Loehr (SIAM J. Discrete Math., 2010).