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Computing the continuous discretely : integer-point enumeration in polyhedra / Matthias Beck and Sinai Robins.

By: Contributor(s): Material type: TextTextSeries: Undergraduate texts in mathematicsPublication details: New York : Springer, 2015.Edition: 2nd edDescription: xx, 285 p. : illustrations ; 25 cmISBN:
  • 9781493929689
Subject(s): DDC classification:
  • 516.11 23 B393
Contents:
1. The Coin-Exchange Problem of Frobenius.- 2. A Gallery of Discrete Volumes.- 3. Counting Lattice Points in Polytopes: The Ehrhart Theory.- 4. Reciprocity.- 5. Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- 6. Magic Squares.- 7. Finite Fourier Analysis.- 8. Dedekind Sums, the Building Blocks of Lattice-Point Enumeration.- 12. Euler-MacLaurin Summation in Rd.- 13. Solid Angles.- 14. A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix: Vertex and Hyperplane descriptions of polytopes.- Hints for Exercises.- References.- List of Symbols.- Index.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 516.11 B393 (Browse shelf(Opens below)) Available 136769
Total holds: 0

Includes bibliographical references and index.

1. The Coin-Exchange Problem of Frobenius.-
2. A Gallery of Discrete Volumes.-
3. Counting Lattice Points in Polytopes: The Ehrhart Theory.-
4. Reciprocity.-
5. Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.-
6. Magic Squares.-
7. Finite Fourier Analysis.-
8. Dedekind Sums, the Building Blocks of Lattice-Point Enumeration.-
12. Euler-MacLaurin Summation in Rd.-
13. Solid Angles.-
14. A Discrete Version of Green's Theorem Using Elliptic Functions.-
Appendix: Vertex and Hyperplane descriptions of polytopes.-
Hints for Exercises.-
References.-
List of Symbols.-
Index.

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.

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