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.
Publisher
University of Wyoming Libraries
Subject
Algebra and Number Theory
Cited by
6 articles.
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