2024/05/27 by Oliver Pechenik, Pechenik, Oliver, Matthew St. Denis +1
Computer Science · Mathematics · #05E05 #05E40 #13C40 #14M15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2405.17645
openalex publication_date 2024/05/27 · openalex created_date 2024/05/30 · openalex updated_date 2026/08/01
We prove a formula for the degrees of Ikeda and Naruse's P-Grothendieck polynomials using combinatorics of shifted tableaux. We show this formula can be used in conjunction with results of Hamaker, Marberg, and Pawlowski to obtain an upper bound on the Castelnuovo-Mumford regularity of certain Pfaffian varieties known as vexillary skew-symmetric matrix Schubert varieties. Similar combinatorics additionally yields a new formula for the degree of Grassmannian Grothendieck polynomials and the regularity of Grassmannian matrix Schubert varieties, complementing a 2021 formula of Rajchgot, Ren, Robichaux, St. Dizier, and Weigandt.