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Bijective proofs for Schur function identities
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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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Cited by 1 Pith paper
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On universal quadratic inequalities for minors of TNN matrices
A quadratic inequality among minors is valid for all totally nonnegative matrices iff, for every feasible planar matching, the matching occurs at least as many times on the left side as on the right.
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