Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations

Details Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Plücker relations

2000-04-17

arxiv.org/abs/math/0004113v2

Mathematics

Combinatorics

Co-author Michael Kleber added a new proof of his theorem by inclusion-exclusion

Scientific paper

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.

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