Computing the Continuous Discretely Integer-Point Enumeration in Polyhedra /

• Main Authors: Beck, Matthias (Author), Robins, Sinai (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Subjects: Mathematics.; Computer mathematics.; Geometry.; Convex geometry.; Discrete geometry.; Number theory.; Discrete mathematics.; Combinatorics.; Discrete Mathematics.; Number Theory.; Convex and Discrete Geometry.; Computational Science and Engineering.

This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is n...

Table of Contents:

• The Essentials of Discrete Volume Computations
• The Coin-Exchange Problem of Frobenius
• A Gallery of Discrete Volumes
• Counting Lattice Points in Polytopes:The Ehrhart Theory
• Reciprocity
• Face Numbers and the Dehn—Sommerville Relations in Ehrhartian Terms
• Magic Squares
• Beyond the Basics
• Finite Fourier Analysis
• Dedekind Sums, the Building Blocks of Lattice-point Enumeration
• The Decomposition of a Polytope into Its Cones
• Euler—Maclaurin Summation in ?d
• Solid Angles
• A Discrete Version of Green’s Theorem Using Elliptic Functions.