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arXiv · 1512.07768

Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities

Yunhi Cho·Seonhwa Kim
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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.

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Yunhi Cho, Seonhwa Kim. 2022-05-10. Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities. https://arxiv.org/abs/1512.07768

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