Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Pl\"ucker relations

Abstract

We present a ``method'' for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi--Trudi identity. We illustrate this ``method'' by generalizing a bijective construction (which was first used by Goulden) to a class of Schur function identities, from which we shall obtain bijective proofs for Dodgson's condensation formula, Pl\"ucker relations and a recent identity of the second author.Comment: Co-author Michael Kleber added a new proof of his theorem by inclusion-exclusio