Hook formulas for skew shapes IV. Increasing tableaux and factorial Grothendieck polynomials

2021/08/23 by Alejandro H. Morales, Morales, Alejandro H., Igor Pak +3
Mathematics · #05A10 (Secondary) #05A15 (Primary) 05E10 #05A20 #05E05 #05E14 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2108.10140

openalex publication_date 2021/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new family of hook-length formulas for the number of standard increasing tableaux which arise in the study of factorial Grothendieck polynomials. In the case of straight shapes our formulas generalize the classical hook-length formula and Stanley's formula. For skew shapes, our formulas generalize the Naruse hook-length formula and its q-analogues, which were studied in previous papers of the series.

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