Bijective proofs of skew Schur polynomial factorizations
نویسندگان
چکیده
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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is not obvious as a relation among the integers, but has a natural bijective explanation. Namely, let Sk be the set of k-subsets of [n]. (Here, [n] denotes the set of positive integers less than or equal to n.) Then |Sk| = n! k!(n−k)! , so the left side of the identity is ∑n k=0 |Sk|. Since the sets Sk are disjoint, this is equal to | ⋃n k=0 Sk| = |P([n])| = 2 , which completes the proof. Of co...
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We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.
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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 re...
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In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F -multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F -multiplicity free quasisy...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2020.105241