Jacobi-Trudi formulas for flagged refined dual stable Grothendieck polynomialsopen access
- Authors
- Kim, J.S.[Kim, J.S.]
- Issue Date
- 2022
- Publisher
- Centre Mersenne
- Keywords
- Grothendieck polynomial; Jacobi-Trudi formula; symmetric function
- Citation
- Algebraic Combinatorics, v.5, no.1, pp.121 - 148
- Indexed
- SCOPUS
- Journal Title
- Algebraic Combinatorics
- Volume
- 5
- Number
- 1
- Start Page
- 121
- End Page
- 148
- URI
- https://scholarworks.bwise.kr/skku/handle/2021.sw.skku/97334
- DOI
- 10.5802/ALCO.203
- ISSN
- 2589-5486
- Abstract
- Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in x = (x1, x2,...) with additional parameters t = (t1, t2,...). The refined dual stable Grothendieck polynomials are defined as a generating function for reverse plane partitions of a given shape. They interpolate between Schur functions and dual stable Grothendieck polynomials introduced by Lam and Pylyavskyy in 2007. Flagged refined dual stable Grothendieck polynomials are a more refined version of refined dual stable Grothendieck polynomials, where lower and upper bounds are given for the entries of each row or column. In this paper Jacobi-Trudi-type formulas for flagged refined dual stable Grothendieck polynomials are proved using plethystic substitution. This resolves a conjecture of Grinberg and generalizes a result by Iwao and Amanov-Yeliussizov. © 2022 Centre Mersenne. All right reserved.
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