Integer Points in Polyhedra

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	FrontmatterDownload pp. i–iv
	PrefaceDownload p. v
	ContentsDownload pp. vii–viii
1	IntroductionDownload pp. 1–7
2	The algebra of polyhedrapp. 9–17
3	Linear transformations and polyhedrapp. 19–26
4	The structure of polyhedrapp. 27–39
5	Polaritypp. 41–47
6	Tangent cones. Decompositions modulo polyhedra with linespp. 49–56
7	Open polyhedrapp. 57–61
8	The exponential valuationpp. 63–75
9	Computing volumespp. 77–79
10	Lattices, bases, and parallelepipedspp. 81–93
11	The Minkowski Convex Body Theorempp. 95–98
12	Reduced basispp. 99–106
13	Exponential sums and generating functionspp. 107–120
14	Totally unimodular polytopespp. 121–128
15	Decomposing a 2-dimensional cone into unimodular cones via continued fractionspp. 129–135
16	Decomposing a rational cone of an arbitrary dimension into unimodular conespp. 137–148
17	Efficient counting of integer points in rational polytopespp. 149–153
18	The polynomial behavior of the number of integer points in polytopespp. 155–165
19	A valuation on rational conespp. 167–182
20	A “local” formula for the number of integer points in a polytopepp. 183–185
	Bibliographypp. 187–189
	Indexp. 191