Computing the Continuous Discretely : Integer-point Enumeration in Polyhedra

Computing the Continuous Discretely Integer-point Enumeration in Polyhedra

This much-anticipated 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. Because there is n...

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Bibliographic Details
Main Authors: Beck, Matthias. author (author), Robins, Sinai. author
Format: eBook
Language:Inglés
Published: New York, NY : Springer New York 2007.
Edition:1st ed. 2007.
Series:Undergraduate Texts in Mathematics,
Subjects:
Combinatorics.
Geometry.
Discrete mathematics.
Number theory.
Convex geometry .
Discrete geometry.
Computer mathematics.
Discrete Mathematics.
Number Theory.
Convex and Discrete Geometry.
Computational Science and Engineering.
See on Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009462128106719
Table of Contents:
  • The Essentials of Discrete Volume Computations
  • 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
  • Beyond the Basics
  • Finite Fourier Analysis
  • Dedekind Sums, the Building Blocks of Lattice-point Enumeration
  • The Decomposition of a Polytope into Its Cones
  • Euler—Maclaurin Summation in ?d
  • Solid Angles
  • A Discrete Version of Green’s Theorem Using Elliptic Functions.

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