Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra

Authors: Matthias Beck, Sinai Robins
Publisher: Springer
Edition: 1
Publish Year: 2007
ISBN: 9780387291390

This 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. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.