论文标题
来自Schur和对称Grothendieck多项式的晶格多型
Lattice polytopes from Schur and symmetric Grothendieck polynomials
论文作者
论文摘要
鉴于晶格多面体的家族，Ehrhart理论中的两个常见问题正在确定何时多层具有整数分解属性，并确定何时多层反射性。尽管这些属性具有独立感兴趣，但由于对$ h^\ ast $ - 多种元素的单程性的猜想，这些属性的汇合是主动调查的来源。在本文中，我们考虑了由代数组合中的两个多项式族引起的牛顿多面体：schur多项式和膨胀的对称的格罗氏多项式多项式。在这两种情况下，我们都证明，通过使用两个多项式家族都饱和牛顿多层室的事实，这些多面体具有整数分解特性。此外，在这两种情况下，我们都提供了这些多面体反射性何时的完整表征。我们以$ h^\ ast $ - vector的一些明确的公式和单型的影响，在schur多项式中。
Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the confluence of these properties is a source of active investigation due to conjectures regarding the unimodality of the $h^\ast$-polynomial. In this paper, we consider the Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomials. In both cases, we prove that these polytopes have the integer decomposition property by using the fact that both families of polynomials have saturated Newton polytope. Furthermore, in both cases, we provide a complete characterization of when these polytopes are reflexive. We conclude with some explicit formulas and unimodality implications of the $h^\ast$-vector in the case of Schur polynomials.
