Slices, slabs, and sections of the unit hypercube
度量几何
2008-02-12 v2 组合数学
摘要
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.
引用
@article{arxiv.math/0607715,
title = {Slices, slabs, and sections of the unit hypercube},
author = {Jean-Luc Marichal and Michael J. Mossinghoff},
journal= {arXiv preprint arXiv:math/0607715},
year = {2008}
}
备注
11 pages; minor corrections to references