Cover Image

Integer points in polyhedra /

Bibliographic Details
Main Author: Barvinok, Alexander, 1963-
Format: Book
Language:English
Published: Zurich : European Mathematical Society, 2008.
Series:Zurich lectures in advanced mathematics.
Subjects:
Polyhedral functions.
Lattice theory.
Polynomials.
Table of Contents:
  • The algebra of polyhedra
  • Linear transformations and polyhedra
  • The structure of polyhedra
  • Polarity
  • Tangent cones : decompositions modulo polyhedra with lines
  • Open polyhedra
  • The exponential valuation
  • Computing volumes
  • Lattices, bases, and parallelepipeds
  • The Minkowski convex body theorem
  • Reduced basis
  • Exponential sums and generating functions
  • Totally unimodular polytopes
  • Decomposing a 2-dimensional cone into unimodular cones via continued fractions
  • Decomposing a rational cone of an arbitrary dimension into unimodular cones
  • Efficient counting of integer points in rational polytopes
  • The polynomial behavior of the number of integer points in polytopes
  • A valuation on rational cones
  • A "local" formula for the number of integer points in a polytope.