论文标题
Jacobi - 用于标记的精制双重稳定Grothendieck多项式的Trudi公式
Jacobi--Trudi formulas for flagged refined dual stable Grothendieck polynomials
论文作者
论文摘要
最近，Galashin，Grinberg和Liu引入了精制的双重稳定Grothendieck多项式，它们是$ x =（x_1，x_2，\ dots）$的对称函数，带有附加参数$ t =（t_1，t_1，t_2，t_2，\ dots）$。精制的双重稳定Grothendieck多项式定义为给定形状的反向平面分区的生成函数。它们在Schur函数和2007年引入的Schur函数和双重稳定的Grothendieck多项式中。标记的精制双重稳定稳定的Grothendieck多项式是更精致的双重稳定稳定的稳定稳定的Grothendieck polymials，在其中为每个列或列的上限提供了下部和上限。在本文中，使用多个替代品证明了标记的精制双重稳定的Grothendieck多项式的Trudi-Type公式。这解决了格林伯格的猜想，并概括了Iwao和Amanov-Yeliussizov的结果。
Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. 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.
