精制Ehrhart系列和加强型环

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica Pub Date : 2023-10-24 DOI:10.1556/012.2023.01541

Praise Adeyemo, Balázs Szendrői

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引用次数: 0

摘要

我们研究了由Chapoton首先考虑的闭多面体的Ehrhart级数的自然精化集。我们用交换代数计算了维数为𝑑的单纯形、维数为𝑑的交叉多面体和维数为𝑑≤3的超立方体的完全一般精炼级数。我们用不同的参数推导出𝑞-integers的乘积的求和公式，推广了MacMahon和Carlitz的经典恒等式。我们也给出了某一精化欧拉多项式的代数性质。

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Refined Ehrhart Series and Bigraded Rings

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 ≤ 3, 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.

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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.