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Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope. (English) Zbl 1162.52008

Beck, Matthias (ed.) et al., Integer points in polyhedra—geometry, number theory, algebra, optimization, statistics. Proceedings of the AMS-IMS-SIAM joint summer research conference, Snowbird, UT, USA, June 11–15, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4173-0/pbk). Contemporary Mathematics 452, 15-33 (2008).
The authors extend to the case of mixed valuations the Euler-Maclaurin expansion of the generating series of a rational polytope obtained previously by the last two authors. This expansion is studied for Barvinok valuations. The generalization leads to methods of computing the highest coefficients of the Ehrhart quasipolynomial of a rational simplex.
For the entire collection see [Zbl 1135.52001].

MSC:

52B45 Dissections and valuations (Hilbert’s third problem, etc.)
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)

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