Intersection bodies of polytopes: translations and convexity

IF 0.6 3区数学 Q3 MATHEMATICS Journal of Algebraic Combinatorics Pub Date : 2024-05-09 DOI:10.1007/s10801-024-01328-9

Marie-Charlotte Brandenburg, Chiara Meroni

引用次数: 0

Abstract

We continue the study of intersection bodies of polytopes, focusing on the behavior of IP under translations of P. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of $I(P+t)$ can be extended to polynomials in variables $t\in \mathbb {R}^d$ within each region of the arrangement. In dimension 2, we give a full characterization of those polygons such that their intersection body is convex. We give a partial characterization for general dimensions.

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多边形的交点体：平移和凸性

我们继续研究多边形的交点体，重点关注 IP 在 P 的平移下的行为。我们引入了仿射超平面排列，并证明描述 $I(P+t)$ 边界的多项式可以扩展为排列的每个区域内变量 $t\in \mathbb {R}^d$ 的多项式。在维度 2 中，我们给出了这些多边形的全部特征，即它们的交点体是凸的。我们给出了一般维度的部分特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.

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