Slices, slabs, and sections of the unit hypercube

Reference : Slices, slabs, and sections of the unit hypercube


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/2415

Title :	Slices, slabs, and sections of the unit hypercube
Language :	English
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]
Publication date :	2008
Journal title :	Online Journal of Analytic Combinatorics
Publisher :	University of Missouri
Volume :	3
Pages :	1-11
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	1931-3365
City :	Columbia
Country :	MO
Keywords :	[en] 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.
Funders :	University of Luxembourg - UL
Name of the research project :	Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/2415
Other URL :	http://analytic-combinatorics.org/index.php/ojac/article/view/26
	http://arxiv.org/abs/math/0607715

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Open access	CubeSlices.pdf	No commentary	Author postprint	211.17 kB	View/Open
Open access	PV-CubeSlices.pdf		Publisher postprint	180.32 kB	View/Open

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Open access	CubeSlicesAMS.pdf	Author postprint (alternative version)	227.26 kB	View/Open

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