Contents

Online Journal of Analytic Combinatorics

  • Research article

Slices, slabs, and sections of the unit hypercube

Jean-Luc Marichal 1, Michael J. Mossinghoff 2
1Institute of Mathematics University of Luxembourg 162A, avenue de la Fa¨ıencerie L-1511 Luxembourg Luxembourg
2Department of Mathematics Davidson College Davidson, NC 28035-6996 USA
  • Received: 27/05/2006
  • Revised: 06/08/2007
  • Accepted: 21/01/2008
  • Published: 29/01/2008

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.

Keywords: Cube slicing, hyperplane section, signed decomposition, volume, Eulerian numbers
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Citation
Jean-Luc Marichal , Michael J. Mossinghoff . Slices, slabs, and sections of the unit hypercube[J], Online Journal of Analytic Combinatorics, Issue 3, 2008. -. DOI: .