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Slices, slabs, and sections of the unit hypercube

By Jean-luc Marichal and Michael J. Mossinghoff

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 Pólya’s Ph.D. thesis, and we discuss several applications of these formulas

Topics: Subject Class, Primary, 52A38, 52B11, Secondary, 05A19, 60D05. Keywords, Cube slicing, hyperplane section, signed decomposition, volume, Eulerian numbers
Year: 2006
OAI identifier: oai:CiteSeerX.psu:10.1.1.186.6671
Provided by: CiteSeerX
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