Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra

by Matthias Beck

Preface.- The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- The Decomposition of a Polytope into Its Cones.- Euler-MacLaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix Triangulations of Polytopes.- Appendix Hints for Selected Exercises.- References.- Index.- List of Symbols.-

Genres: Mathematics

308 pages, Paperback

First published December 6, 2006