Computing the Continuous Discretely

Integer-Point Enumeration in Polyhedra

Matthias Beck, Sinai Robins

242 pages, parution le 01/01/2007

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Résumé

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.

Written for: Undergraduate and graduate math students

Sommaire

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
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 A: Triangulations of Polytopes
Appendix B: Hints for Selected Exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Matthias Beck, Sinai Robins
Parution	01/01/2007
Nb. de pages	242
Format	16 x 24
Couverture	Relié
Intérieur	Noir et Blanc
EAN13	9780387291390
ISBN13	978-0-387-29139-0