cube slicing; hyperplane section; signed decomposition; volume; Eulerian numbers
Abstract :
[en] Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a half-space, 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.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2010-397
Author, co-author :
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mossinghoff, Michael J.; Davidson College, Davidson, NC, USA > Department of Mathematics
Language :
English
Title :
Slices, slabs, and sections of the unit hypercube
Publication date :
2008
Journal title :
Online Journal of Analytic Combinatorics
ISSN :
1931-3365
Publisher :
University of Missouri, Columbia, United States - Missouri
