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Slices, slabs, and sections of the unit hypercube

Jean-Luc Marichal·Michael J. Mossinghoff
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Abstract

Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these problems, dating to Polya's Ph.D. thesis, and we discuss several applications of these formulas.

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Jean-Luc Marichal, Michael J. Mossinghoff. 2008-02-12. Slices, slabs, and sections of the unit hypercube. https://arxiv.org/abs/math/0607715

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