Integer Points in Polyhedra

  • Alexander Barvinok

    University of Michigan, Ann Arbor, USA
Integer Points in Polyhedra cover

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