Integer Points in Polyhedra

, by Beck, Matthias; Haase, Christian; Reznick, Bruce; Vergne, Michele; Welker, Volkmar

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ISBN: 9780821841730 | 0821841734
Cover: Paperback
Copyright: 4/13/2008

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The volume is a cross section of recent advances connected to lattice-point questions. Topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for resarchers and graduate students interested in combinatorial aspects of the above fields.

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Lattice reformulation of integer programming problems
Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope
Combinatorial aspects of mirror symmetry
Ehrhart polynomial roots and Stanley's non-negativity theorem
Enumeration of integer solutions to linear inequalities defined by digraphs
Perfect Delaunay polytopes and perfect quadratic functions on lattices
Quasi-period collapse and $GL_n(\mathbb{Z})$-scissors congruence in rational polytopes
Quadratic Grobner bases arising from combinatorics
Ehrhart analogue of the $h$-vector
Saturation points on faces of a rational polyhedral cone
An explicit formulation for two dimensional vector partition functions
Let me tell you my favorite lattice-point problem...
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Integer Points in Polyhedra

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