Integer points in polyhedra / Alexander Barvinok.

• 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.

Ämnesord

Polyhedral functions.  (LCSH)

Lattice theory.  (LCSH)

Polynomials.  (LCSH)

Polyeder.  (swd)

Klassifikation

QA171.5 (LCC)

52-02 (msc)

05A15 (msc)

11H06 (msc)

52B20 (msc)

52C07 (msc)