Cell complexities in hyperplane arrangements

Boris Aronov; Micha Sharir

doi:10.1007/s00454-003-0854-z

Cell complexities in hyperplane arrangements

Boris Aronov, Micha Sharir

Research output: Contribution to journal › Article › peer-review

Abstract

We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matoušek, and Sharir, on the sum of squares of cell complexities in such an arrangement.

Original language	English (US)
Pages (from-to)	107-115
Number of pages	9
Journal	Discrete and Computational Geometry
Volume	32
Issue number	1
DOIs	https://doi.org/10.1007/s00454-003-0854-z
State	Published - Jul 2004

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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abstract = "We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matou{\v s}ek, and Sharir, on the sum of squares of cell complexities in such an arrangement.",

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Cell complexities in hyperplane arrangements

Abstract

ASJC Scopus subject areas

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