Jacobi–Trudi formulas for flagged refined dual stable Grothendieck polynomials
Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 121-148.

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in x=(x 1 ,x 2 ,...) with additional parameters t=(t 1 ,t 2 ,...). 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.

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DOI: 10.5802/alco.203
Classification: 05E05,  05A15,  05E10
Keywords: Jacobi–Trudi formula, Grothendieck polynomial, symmetric function
Kim, Jang Soo 1

1 Department of Mathematics Sungkyunkwan University (SKKU) Suwon Gyeonggi-do 16419 South Korea
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Kim, Jang Soo. Jacobi–Trudi formulas for flagged refined dual stable Grothendieck polynomials. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 121-148. doi : 10.5802/alco.203. https://alco.centre-mersenne.org/articles/10.5802/alco.203/

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