Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Pl\"ucker relations
Combinatorics
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0004113,
title = {Bijective proofs for Schur function identities which imply Dodgson's condensation formula and Pl\"ucker relations},
author = {Markus Fulmek and Michael Kleber},
journal= {arXiv preprint arXiv:math/0004113},
year = {2007}
}
Comments
Co-author Michael Kleber added a new proof of his theorem by inclusion-exclusion