正常复合物的混合体积

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry Pub Date : 2024-06-04 DOI:10.1007/s00454-024-00662-w

Lauren Nowak, Patrick O’Melveny, Dustin Ross

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引用次数: 0

摘要

正态复数是简单扇形的正交截断。在本文中，我们发展了对正复数混合体积的研究。我们的主要结果是一个充分条件，它确保与给定扇形相关的正复数的混合体积满足亚历山德罗夫-芬切尔不等式。通过专门研究矩阵的伯格曼扇形，我们给出了作为正复数亚历山德罗夫-芬切尔不等式后果的希伦-罗塔-韦尔什猜想的新证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Mixed Volumes of Normal Complexes

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Mixed Volumes of Normal Complexes

Normal complexes are orthogonal truncations of simplicial fans. In this paper, we develop the study of mixed volumes for normal complexes. Our main result is a sufficiency condition that ensures when the mixed volumes of normal complexes associated to a given fan satisfy the Alexandrov–Fenchel inequalities. By specializing to Bergman fans of matroids, we give a new proof of the Heron–Rota–Welsh Conjecture as a consequence of the Alexandrov–Fenchel inequalities for normal complexes.

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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.