Integer points in polyhedra
By: Alexander Barvinok
Series: Zurich lectures in advanced mathematics
Publisher: European Mathematical Society
Published: 2008
Place of publication: Zurich
Language: eng
Number of pages: 189
ISBN-13: 9783037190524
Subjects: Partiële orde; Polynomials; Convexe lichamen; Polyeder; Getaltheorie; Polyhedral functions; Lattice theory; Veelvlakken
Notes: Includes bibliographical references (p. [187]-189) and index.
Table of contents: title: The algebra of polyhedra; title: Linear transformations and polyhedra; title: The structure of polyhedra; title: Polarity; title: Tangent cones : decompositions modulo polyhedra with lines; title: Open polyhedra; title: The exponential valuation; title: Computing volumes; title: Lattices, bases, and parallelepipeds; title: The Minkowski convex body theorem; title: Reduced basis; title: Exponential sums and generating functions; title: Totally unimodular polytopes; title: Decomposing a 2-dimensional cone into unimodular cones via continued fractions; title: Decomposing a rational cone of an arbitrary dimension into unimodular cones; title: Efficient counting of integer points in rational polytopes; title: The polynomial behavior of the number of integer points in polytopes; title: A valuation on rational cones; title: A "local" formula for the number of integer points in a polytope.