Book 2007

Computing the Continuous Discretely

Integer-Point Enumeration in Polyhedra

Authors:

ISBN: 978-0-387-29139-0 (Print) 978-0-387-46112-0 (Online)

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii

  2. The Essentials of Discrete Volume Computations

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      Chapter

      Pages 3-24

      The Coin-Exchange Problem of Frobenius

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      Chapter

      Pages 25-55

      A Gallery of Discrete Volumes

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      Chapter

      Pages 57-82

      Counting Lattice Points in Polytopes:The Ehrhart Theory

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      Chapter

      Pages 83-93

      Reciprocity

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      Chapter

      Pages 95-104

      Face Numbers and the Dehn—Sommerville Relations in Ehrhartian Terms

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      Chapter

      Pages 105-120

      Magic Squares

  3. Beyond the Basics

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      Chapter

      Pages 123-137

      Finite Fourier Analysis

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      Chapter

      Pages 139-153

      Dedekind Sums, the Building Blocks of Lattice-point Enumeration

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      Chapter

      Pages 155-165

      The Decomposition of a Polytope into Its Cones

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      Chapter

      Pages 167-178

      Euler—Maclaurin Summation in ℝ d

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      Chapter

      Pages 179-190

      Solid Angles

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      Chapter

      Pages 191-197

      A Discrete Version of Green’s Theorem Using Elliptic Functions

  4. Back Matter

    Pages 199-234