Bijective proofs for Schur function identities

Details Bijective proofs for Schur function identities Bijective proofs for Schur function identities

2009-09-29

arxiv.org/abs/0909.5334v1

Mathematics

Combinatorics

Scientific paper

Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in a paper by Fulmek and Kleber, where it was used to prove bijectively Dodgsons condensation formula and the Pluecker relations, but was not paid further attention: So we take the opportunity to make obvious the range of applicability of this identity by giving concrete examples, accompanied by many graphical illustrations.

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