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