具有k-平面的刺凸细分

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.025

Alfredo Hubard , Arnau Padrol

引用次数: 0

摘要

我们证明了对于Rd的每一个凸细分为n个单元格，存在一个k平刺Ω((log (n) /log (log)) 1/(d - k))。作为推论，我们推断出每个有n个顶点的d-多边形都有一个具有Ω((log (n) /log (log)) 1/(d - k))顶点的k阴影。

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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Stabbing convex subdivisions with k-flats

We prove that for every convex subdivision of $R^{d}$ into n cells there exists a k-flat stabbing $Ω ({(\log n / \log \log n)}^{1 / (d - k)})$ of them. As a corollary we deduce that every d-polytope with n vertices has a k-shadow with $Ω ({(\log n / \log \log n)}^{1 / (d - k)})$ vertices.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.