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 : Imprint: Springer, 2015.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Computer mathematics.; Convex geometry.; Discrete geometry.; Number theory.; Combinatorics.; Number Theory.; Convex and Discrete Geometry.; Computational Science and Engineering.

This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is pe...

Table of Contents:

• 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
• Finite Fourier Analysis
• Dedekind Sums
• Zonotopes
• h-Polynomials and h*-Polynomials
• 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.