Volume of hypercubes clipped by hyperplanes and combinatorial identities

Yunhi Cho; Seonhwa Kim

doi:10.13001/ela.2020.5085

Volume of hypercubes clipped by hyperplanes and combinatorial identities

Yunhi Cho, Seonhwa Kim

Department of Mathematics

Korea Institute for Advanced Study

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

5 Scopus citations

Abstract

There is an elegant expression for the volume of hypercube [0, 1]ⁿ clipped by a single hyperplane. In the article, the formula is generalized to the case of more than one hyperplane. An important foundation for the result is Lawrence’s formula and a way to weaken two restrictions of simplicity and non-parallelness in his formula is also considered. Several concrete volume formulas of clipped hypercubes are derived explicitly and the corresponding combinatorial identities are obtained as an application.

Original language	English
Pages (from-to)	228-255
Number of pages	28
Journal	Electronic Journal of Linear Algebra
Volume	36
Issue number	1
DOIs	https://doi.org/10.13001/ela.2020.5085
State	Published - 2020

Keywords

Combinatorial identity
Hypercube
Volume

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10.13001/ela.2020.5085

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Volume of hypercubes clipped by hyperplanes and combinatorial identities

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Keywords

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