Maximal integral simplices with no interior integer points

Details Maximal integral simplices with no interior integer points Maximal integral simplices with no interior integer points

2009-04-14

arxiv.org/abs/0904.2108v2

Mathematics

Optimization and Control

Scientific paper

In this paper, we consider integral maximal lattice-free simplices. Such simplices have integer vertices and contain integer points in the relative interior of each of their facets, but no integer point is allowed in the full interior. In dimension three, we show that any integral maximal lattice-free simplex is equivalent to one of seven simplices up to unimodular transformation. For higher dimensions, we demonstrate that the set of integral maximal lattice-free simplices with vertices lying on the coordinate axes is finite. This gives rise to a conjecture that the total number of integral maximal lattice-free simplices is finite for any dimension.

Affiliated with

Also associated with

No associations

Rating

Maximal integral simplices with no interior integer points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Maximal integral simplices with no interior integer points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Maximal integral simplices with no interior integer points will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-98772