论文标题
$β$ - grothendieck多项式的主体专业的模式范围
Pattern bounds for principal specializations of $β$-Grothendieck Polynomials
论文作者
论文摘要
对于Schubert多项式的主要专业$ν_W：= \ Mathfrak s_w（1，\ dots，1）$，最近对下界产生了兴趣。我们证明了Yibo Gao的猜想在$ 1243 $避免排列的情况下，就$ W $中包含的排列模式而言，$ν_W$的下限为$ν_W$。我们将此结果扩展到了$β$ -Grothendieck polyenmials $ν^{（（β）} _ W：= \ Mathfrak g^{（β）} _ w（1，\ dots，1）$，通过限制Vexillary $ 1243 $ avoideventications。我们的方法是培训，是对系数的组合解释$ C_W $和$ C^{（β）} _ W $出现在这些猜想中。
There has been recent interest in lower bounds for the principal specializations of Schubert polynomials $ν_w := \mathfrak S_w(1,\dots,1)$. We prove a conjecture of Yibo Gao in the setting of $1243$-avoiding permutations that gives a lower bound for $ν_w$ in terms of the permutation patterns contained in $w$. We extended this result to principal specializations of $β$-Grothendieck polynomials $ν^{(β)}_w := \mathfrak G^{(β)}_w(1,\dots,1)$ by restricting to the class of vexillary $1243$-avoiding permutations. Our methods are bijective, offering a combinatorial interpretation of the coefficients $c_w$ and $c^{(β)}_w$ appearing in these conjectures.
