Integer points in polyhedra - Barvinok, Alexander 1963- (Zurich European Mathematical Society, 2008)
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.
Includes bibliographical references (pages [187]-189) and index.
Keywords: Polyhedral functions; Lattice theory; Polynomials