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Integer points in convex polyhedra

Known as: Integer points in a convex polyhedron, Z-polyhedra, Integer points in convex polyhedron 
Study of integer points in convex polyhedra is motivated by the questions, such as "how many nonnegative integer-valued solutions does a system of… 
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Related topics

Related topics

9 relations
Computer scienceConvex setEhrhart polynomialLoop optimization

Broader (2)

Linear algebraLinear programming

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2019
2019
Computing the integer points of a polyhedron
The integer points of polyhedral sets are of interest in many areas of mathematical sciences, see for instance the landmark… 
2015
2015
Computer Algebra and Polynomials
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a… 
2010
2010
Counting lattice points in polyhedra using the Ehrhart theory, applied to Voting theory
In an United States presidential election each state has a certain amount of electors. The candidate who obtains the most popular… 
2008
2008
Minimal volume K-point lattice D-simplices
We extend the results of Bey, Hen, and Wills (this http URL). In this paper, we show that, up to equivalence under unimodular… 
2008
2008
COUNTING LATTICE POINTS IN POLYHEDRA
We present Barvinok’s 1994 and 1999 algorithms for counting lattice points in polyhedra. 1. The 1994 algorithm In [2], Barvinok… 
2006
2006
Minkowski decomposition of convex lattice polygons
A relatively recent area of study in geometric modelling concerns toric Bezier patches. In this line of work, several questions… 
1996
1996
Extension of the ALPHA language to recurrences on sparse periodic domains
ALPHA is a functional language based on systems of affine recurrence equations over polyhedral domains. We present an extension… 
1992
1992
On integer points in polyhedra: A lower bound
Given a polyhedronP⊂ℝ we writePI for the convex hull of the integral points inP. It is known thatPI can have at most135-2… 
1991
1991
On Counting Lattice Points in Polyhedra
  • M. Dyer
  • SIAM journal on computing (Print)
  • 1991
  • Corpus ID: 20018045
Some reductions of the computational problem of counting all the integer lattice points in an arbitrary convex polyhedron in a… 
1944
1944
The numerical solution of Laplace’s and Poisson’s equations
Briefly, the method of procedure, commonly called the Liebmann procedure,1 is to cover the region R with a rectangular network of… 
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