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Computing the Continuous Discretely

Integer-Point Enumeration in Polyhedra
Buch | Hardcover
227 Seiten
2007 | 1st ed. 2007. Corr. printing 2007
Springer-Verlag New York Inc.
978-0-387-29139-0 (ISBN)

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Computing the Continuous Discretely - Matthias Beck, Sinai Robins, Nicole Clark
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This much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. It weaves a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory.
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.

Preface.- 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.- References.- Index.- List of Symbols.-

Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo biography
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Gewicht 1170 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Graphentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 0-387-29139-3 / 0387291393
ISBN-13 978-0-387-29139-0 / 9780387291390
Zustand Neuware
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