论文标题
精致的Ehrhart系列和大戒指
Refined Ehrhart series and bigraded rings
论文作者
论文摘要
我们研究了封闭的多型埃尔哈特（Ehrhart）系列的一系列自然改进，该系列首先由肖普顿（Capoton）考虑。我们使用交换代数为Dimension D的简单D尺寸D的简单D d <4分别计算了Dimension d的单纯形d的完整序列。我们推断出具有不同论点的Q-Integers产品的求和公式，从而推广了由于Macmahon和Carlitz引起的经典身份。我们还用代数术语提出了某些精制的欧拉多项式的特征。
We study a natural set of refinements of the Ehrhart series of a closed polytope, first considered by Chapoton. We compute the refined series in full generality for a simplex of dimension d, a cross-polytope of dimension d, respectively a hypercube of dimension d<4, using commutative algebra. We deduce summation formulae for products of q-integers with different arguments, generalizing a classical identity due to MacMahon and Carlitz. We also present a characterisation of a certain refined Eulerian polynomial in algebraic terms.
