论文标题
幻灯片多样性键多项式
Slide multiplicity free key polynomials
论文作者
论文摘要
Schubert多项式由Lascoux-Schützenberger的关键多项式进行了完善，而Assaf-Searles的基本幻灯片多项式又可以完善。在本文中，我们确定了由强组成索引的关键多项式的哪些基本幻灯片多项式改进，无数性。我们还提供了一种递归算法，以确定由强组成组成的关键多项式索引的基本幻灯片多项式改进中的所有术语。从这里开始，我们将结果应用于开始分类哪些基本幻灯片多项式改进，并由弱组成索引，是无数性的。我们完全解决了弱组成最多具有两个非零零件或总和最多两个非零项的情况。
Schubert polynomials are refined by the key polynomials of Lascoux-Schützenberger, which in turn are refined by the fundamental slide polynomials of Assaf-Searles. In this paper we determine which fundamental slide polynomial refinements of key polynomials, indexed by strong compositions, are multiplicity free. We also give a recursive algorithm to determine all terms in the fundamental slide polynomial refinement of a key polynomial indexed by a strong composition. From here, we apply our results to begin to classify which fundamental slide polynomial refinements, indexed by weak compositions, are multiplicity free. We completely resolve the cases when the weak composition has at most two nonzero parts or the sum has at most two nonzero terms.
