Bijective Proofs for Schur Function Identities which Imply Dodgson's Condensation - Formula and Plu"cker Relations
نویسندگان
چکیده
We exhibit 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, Plücker relations and special cases of a theorem of Kleber.
منابع مشابه
Bijective Proofs for Schur Function Identities
In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker 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 [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson’s condensation formula and the Plücker relations, but w...
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عنوان ژورنال:
- Electr. J. Comb.
دوره 8 شماره
صفحات -
تاریخ انتشار 2001