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Barvinok Alexander. Integer Points in Polyhedra

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Barvinok Alexander. Integer Points in Polyhedra
European Mathematical Society, 2008. — 189 p. — (Zurich Lectures in Advanced Mathematics). — ISBN 978-3-03719-052-4.
These are the lecture notes for a graduate course which the author taught twice, first at the ETH, Z¨urich in Spring - Summer 2007 as a part of the “Nachdiplom Lectures” series and then at the University of Michigan, Ann Arbor, in the Fall of 2007 as a regular graduate course with exercises and grades. The goal of the course is by starting from basic linear algebra, to walk the reader towards most recent advances in enumeration of integer points in polyhedra.
Key words: Algebra of polyhedra, Berline–Vergne local formula, continued fractions, Ehrhart polynomial, Euler characteristic, generating functions, integer points, Lenstra–Lenstra–Lovász lattice reduction algorithm, Minkowski Convex Body Theorem.
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