Hook formulas for skew shapes III. Multivariate and product formulas
نویسندگان
چکیده
منابع مشابه
Hook Formulas for Skew Shapes
The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give an algebraic and a combinatorial proof of Naruse’s formula, by using factorial Schur functio...
متن کاملHook formulas for skew shapes I. q-analogues and bijections
The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give an algebraic and a combinatorial proof of Naruse’s formula, by using factorial Schur functio...
متن کاملHook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications
The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In [MPP1] we gave two different q-analogues of Naruse’s formula: for the skew Schur functions, and for counting reverse plane partitions of skew shapes. In this paper we give an elementary proof of Naruse’...
متن کاملHomotopies for Resolutions of Skew-hook Shapes
We present characteristic-free resolutions and splitting homotopies for the Weyl modules associated to skew-hook shapes. Résumé. Nous présentons des résolutions en caractéristique-libre, et des homotopies associées aux formes du type “skew-hook”.
متن کاملWeighted branching formulas for the hook lengths
The famous hook-length formula is a simple consequence of the branching rule for the hook lengths. While the Greene-Nijenhuis-Wilf probabilistic proof is the most famous proof of the rule, it is not completely combinatorial, and a simple bijection was an open problem for a long time. In this extended abstract, we show an elegant bijective argument that proves a stronger, weighted analogue of th...
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ژورنال
عنوان ژورنال: Algebraic Combinatorics
سال: 2019
ISSN: 2589-5486
DOI: 10.5802/alco.67