论文标题
双Grothendieck多项式的组合
Combinatorics of Double Grothendieck Polynomials
论文作者
论文摘要
我们提供了双重格罗氏多项式的广义cauchy身份证明，这是对稳定的双色性多项式的组合解释，从tableaux的三元组来看，以及稳定的双重粒度多项式和稳定的双重稳定稳定稳定稳定的双重稳定的双重粒料。这个所谓的一半弱稳定的双重稳定的Glothendieck多项式评估在$ x = y $中概括了$ b $ b $ stanley对称的对称功能，并且是$ q $ $ -schur的阳性。最后，我们提出了两个开放问题以及关于$ k $ schur $ q $ functions的$ k $理论类似物的猜想。猜想由附录中给出的代码支持。
We give a proof of the generalized Cauchy identity for double Grothendieck polynomials, a combinatorial interpretation of the stable double Grothendieck polynomials in terms of triples of tableaux, and an interpolation between the stable double Grothendieck polynomial and the weak stable double Grothendieck polynomial. This so-called half weak stable double Grothendieck polynomial evaluated at $x=y$ generalizes the type $B$ Stanley symmetric function of Billey and Haiman and is $Q$-Schur positive by degree. We conclude with two open problems as well as a conjecture regarding the $K$-theoretic analogues of factorial Schur $Q$-functions defined by Ikeda and Naruse. The conjecture is supported by code given in the appendices.
