02339nam a22003855a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200170018408400290020110000340023024500770026426000820034130000340042333600260045733700260048333800360050934700240054549000510056950600660062052010190068665000280170565000360173365000380176965000230180765000230183085600320185385600680188579-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080901sz fot ||| 0|eng d a978303719552970a10.4171/0522doi ach0018173 7aPBMZ2bicssc 7aPBRD2bicssc a52-xxa05-xxa11-xx2msc1 aBarvinok, Alexander,eauthor.10aInteger Points in Polyhedrah[electronic resource] /cAlexander Barvinok3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (199 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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–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.07aFinite geometry2bicssc07aAlgebraic number theory2bicssc07aConvex and discrete geometry2msc07aCombinatorics2msc07aNumber theory2msc40uhttps://doi.org/10.4171/052423cover imageuhttps://www.ems-ph.org/img/books/barvinok_mini.jpg