Slices, slabs, and sections of the unit hypercube

Details Slices, slabs, and sections of the unit hypercube Slices, slabs, and sections of the unit hypercube

2006-07-27

arxiv.org/abs/math/0607715v2

Online Journal of Analytic Combinatorics, Issue 3 (2008), #1

Mathematics

Metric Geometry

11 pages; minor corrections to references

Scientific paper

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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