论文标题
在Grothendieck多项式的支持下
On the support of Grothendieck polynomials
论文作者
论文摘要
Grothendieck polynomials $\mathfrak{G}_w$ of permutations $w\in S_n$ were introduced by Lascoux and Schützenberger in 1982 as a set of distinguished representatives for the K-theoretic classes of Schubert cycles in the K-theory of the flag variety of $\mathbb{C}^n$.我们认为，Grothendieck多项式$ \ mathfrak {g} _W $在componentwise比较下形成poset的指数与$ \ mathbb {z}^n $同符的poset形式。当$ w \ in s_n $避免使用一组模式时，我们可以将$ \ mathfrak {g} _W $的系数与上述poset的möbius函数值进行连接，并使用$ \ hat {0} $ $ apped。我们证明了我们对格拉斯曼尼亚和烟花排列的猜想的特殊情况。
Grothendieck polynomials $\mathfrak{G}_w$ of permutations $w\in S_n$ were introduced by Lascoux and Schützenberger in 1982 as a set of distinguished representatives for the K-theoretic classes of Schubert cycles in the K-theory of the flag variety of $\mathbb{C}^n$. We conjecture that the exponents of nonzero terms of the Grothendieck polynomial $\mathfrak{G}_w$ form a poset under componentwise comparison that is isomorphic to an induced subposet of $\mathbb{Z}^n$. When $w\in S_n$ avoids a certain set of patterns, we conjecturally connect the coefficients of $\mathfrak{G}_w$ with the Möbius function values of the aforementioned poset with $\hat{0}$ appended. We prove special cases of our conjectures for Grassmannian and fireworks permutations.
