Reference : Slices, slabs, and sections of the unit hypercube
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Slices, slabs, and sections of the unit hypercube
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mossinghoff, Michael J. mailto [Davidson College, Davidson, NC, USA > Department of Mathematics]
Online Journal of Analytic Combinatorics
University of Missouri
Yes (verified by ORBilu)
[en] cube slicing ; hyperplane section ; signed decomposition ; volume ; Eulerian numbers
[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 PĆ³lya's Ph.D. thesis, and we discuss several applications of these formulas.
University of Luxembourg - UL
Researchers ; Professionals ; Students

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