Counting Integer Points in Higher-Dimensional Polytopes

被引：4

作者：

Barvinok, Alexander ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

CONVEXITY AND CONCENTRATION | 2017年 / 161卷

关键词：

ASYMPTOTIC ENUMERATION; PRESCRIBED ROW; MATRICES; NUMBER; GRAPHS; TABLE;

D O I：

10.1007/978-1-4939-7005-6_20

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We survey some computationally efficient formulas to estimate the number of integer or 0-1 points in polytopes. In many interesting cases, the formulas are asymptotically exact when the dimension of the polytopes grows. The polytopes are defined as the intersection of the non-negative orthant or the unit cube with an affine subspace, while the main ingredient of the formulas comes from solving a convex optimization problem on the polytope.

引用

页码：585 / 612

页数：28

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