Slices , Slabs , and Sections of the Unit Hypercube

  title={Slices , Slabs , and Sections of the Unit Hypercube},
  author={Jean-Luc Marichal and Michael J. Mossinghoff},
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. 
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