Hook 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’...

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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...

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Hook 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...

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Combinatorial Proofs of Hook Generating Functions for Skew Plane Partitions

Sagan, B.E., Combinatorial proofs of hook generating functions for skew plane partitions, Theoretical Computer Science 117 (1993) 273-287. We provide combinatorial proofs of two hook generating functions for skew plane partitions. One proof involves the Hillman-Grass1 (1976) algorithm and the other uses a modification of Schiitzenberger’s (1963, 1977) “jeu de taquin” due to Kadell (to appear). ...

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Homotopies 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”.

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Hook Formulas for Skew Shapes II. Combinatorial Proofs and Enumerative Applications

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