论文标题
关于Grothendieck多项式的程度
On the degree of Grothendieck polynomials
论文作者
论文摘要
Pechenik，Speyer和Weigandt（2021）最近给出了Grothendieck多项式的美丽学位公式。我们利用Lenart，Robinson和Sottile（2006）引入的Grothendieck多项式的攀爬链模型提供了其学位公式的替代证明。此外，对于满足$ x_1 <x_2 <x_n $的任何定期顺序，我们介绍了Grothendieck多项式$ \ mathfrak {g} _W（x_1，x_1，\ ldots，x_n）$，使Hafner的（20222222222222）的每个同质组件的主要单一元素。我们以$ \ mathfrak {g} _W（x_1，\ ldots，x_n）$的统一组件的领先单元的猜想结束。
A beautiful degree formula for the Grothendieck polynomials was recently given by Pechenik, Speyer, and Weigandt (2021). We provide an alternative proof of their degree formula, utilizing the climbing chain model for Grothendieck polynomials introduced by Lenart, Robinson, and Sottile (2006). Moreover, for any term order satisfying $x_1<x_2<\cdots<x_n$ we present the leading monomial of each homogeneous components of the Grothendieck polynomial $\mathfrak{G}_w(x_1,\ldots,x_n)$, confirming a conjecture of Hafner (2022). We conclude with a conjecture for the leading monomials of the homogenegous components of $\mathfrak{G}_w(x_1,\ldots,x_n)$ in any term order satisfying $x_1>x_2>\cdots>x_n$.
