论文标题
滑动多项式和子字络合物
Slide polynomials and subword complexes
论文作者
论文摘要
子单词复合物由A.knutson和E.Miller在2004年定义，用于描述基质舒伯特品种的Gröbner变性。这种复杂的方面是由梦想的梦想所索引的，或者是由相应的舒伯特多项式中的单一群体索引。在2017年，S.Assaf和D.Searles定义了幻灯片多项式的基础，概括了Stanley对称函数，并描述了在此基础上扩展Schubert多项式的组合规则。我们将子单词复合物分解为称为幻灯片复合物的地层，该分层与幻灯片多项式相对应。幻灯片复合物显示出对球或球的同构。
Subword complexes were defined by A.Knutson and E.Miller in 2004 for describing Gröbner degenerations of matrix Schubert varieties. The facets of such a complex are indexed by pipe dreams, or, equivalently, by the monomials in the corresponding Schubert polynomial. In 2017 S.Assaf and D.Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and described a combinatorial rule for expanding Schubert polynomials in this basis. We describe a decomposition of subword complexes into strata called slide complexes, that correspond to slide polynomials. The slide complexes are shown to be homeomorphic to balls or spheres.
