02426nam 22004575a 450 991015193440332120091109150325.03-03719-552-510.4171/052(CKB)3710000000953831(CH-001817-3)79-091109(PPN)178155489(EXLCZ)99371000000095383120091109j20080901 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierInteger Points in Polyhedra[electronic resource] /Alexander BarvinokZuerich, Switzerland European Mathematical Society Publishing House20081 online resource (199 pages)Zurich Lectures in Advanced Mathematics (ZLAM)This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra- Lenstra-Lovász lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.Finite geometrybicsscAlgebraic number theorybicsscConvex and discrete geometrymscCombinatoricsmscNumber theorymscFinite geometryAlgebraic number theoryConvex and discrete geometryCombinatoricsNumber theory52-xx05-xx11-xxmscBarvinok Alexander322075ch0018173BOOK9910151934403321Integer points in polyhedra229594UNINA