Computing the Ehrhart quasi-polynomial of a rational simplex

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dc.creatorBarvinok, Alexander
dc.date2005-04-21
dc.date.accessioned2026-07-07T05:19:19Z
dc.date.available2026-07-07T05:19:19Z
dc.descriptionWe present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms were known for integer simplices and for rational polytopes of a fixed dimension. The algorithm is based on the formula relating the kth coefficient of the Ehrhart quasi-polynomial of a rational polytope to volumes of sections of the polytope by affine lattice subspaces parallel to k-dimensional faces of the polytope. We discuss possible extensions and open questions.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0504444
dc.identifierhttp://arxiv.org/abs/math/0504444
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74980
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.subject52C07, 05A15, 68R05
dc.titleComputing the Ehrhart quasi-polynomial of a rational simplex
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