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Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra

โœ Scribed by Matthias Beck, Sinai Robins

Publisher
Springer
Year
2007
Tongue
English
Leaves
253
Series
Undergraduate Texts in Mathematics
Category
Library
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โœฆ Synopsis

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.

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<p>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