Stabbing convex subdivisions with k-flats

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

Abstract

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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具有k-平面的刺凸细分

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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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

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