Hook Formulas for Skew Shapes IV. Increasing Tableaux and Factorial Grothendieck Polynomials
نویسندگان
چکیده
We present a new family of hook-length formulas for the number standard increasing tableaux which arise in study factorial Grothendieck polynomials. In case straight shapes our generalize classical formula and Stanley's formula. For skew shapes, Naruse its $q$-analogues, were studied previous papers series.
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 کاملFactorial Grothendieck Polynomials
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a generalisation of a Littlewood-Richardson rule for Grothendieck polynomials.
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 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’...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05777-0