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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aInteger Points in Polyhedra$b[electronic resource] /$fAlexander Barvinok
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008
215   $a1 online resource (199 pages)
225 0 $aZurich Lectures in Advanced Mathematics (ZLAM)
330   $aThis 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-Lova?sz 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.
606   $aFinite geometry$2bicssc
606   $aAlgebraic number theory$2bicssc
606   $aConvex and discrete geometry$2msc
606   $aCombinatorics$2msc
606   $aNumber theory$2msc
615 07$aFinite geometry
615 07$aAlgebraic number theory
615 07$aConvex and discrete geometry
615 07$aCombinatorics
615 07$aNumber theory
686   $a52-xx$a05-xx$a11-xx$2msc
700   $aBarvinok$b Alexander$0322075
801  0$bch0018173
906   $aBOOK
912   $a9910151934403321
996   $aInteger points in polyhedra$9229594
997   $aUNINA