# ALGEBRAIC COMBINATORICS

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 $x=\left({x}_{1},{x}_{2},...\right)$ with additional parameters $t=\left({t}_{1},{t}_{2},...\right)$. 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.

Accepted:
Revised after acceptance:
Published online:
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
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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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