Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities
Combinatorics
2022-05-11 v4 Optimization and Control
Abstract
There is an elegant expression for the volume of hypercube 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.
Cite
@article{arxiv.1512.07768,
title = {Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities},
author = {Yunhi Cho and Seonhwa Kim},
journal= {arXiv preprint arXiv:1512.07768},
year = {2022}
}