Integer Points in Polyhedra

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European Mathematical Society, 2008 - Mathematics - 189 pages
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Contents

Introduction
1
The algebra of polyhedra
9
Linear transformations and polyhedra
19
The structure of polyhedra
27
Polarity
41
Tangent cones Decompositions modulo polyhedra with lines
49
Open polyhedra
57
The exponential valuation
63
The Minkowski Convex Body Theorem
95
Reduced basis
99
Exponential sums and generating functions
107
Totally unimodular polytopes
121
Decomposing a 2dimensional cone into unimodular cones via continued fractions
129
Decomposing a rational cone of an arbitrary dimension into unimodular cones
137
viii
149
A valuation on rational cones
167

Computing volumes
77
Lattices bases and parallelepipeds
81
A local formula for the number of integer points
183
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