Name
Abstract | ||
|---|---|---|
The Minkowski length of a lattice polytope P is a natural generalization of the lattice diameter of P . It can be defined as the largest number of lattice segments whose Minkowski sum is contained in P . The famous Ehrhart theorem states that the number of lattice points in the positive integer dilates t P of a lattice polytope P behaves polynomially in t ź N . In this paper we prove that for any lattice polytope P , the Minkowski length of t P for t ź N is eventually a quasi-polynomial with linear constituents. We also give a formula for the Minkowski length of coordinates boxes, degree one polytopes, and dilates of unimodular simplices. In addition, we give a new bound for the Minkowski length of lattice polygons and show that the Minkowski length of a lattice triangle coincides with its lattice diameter. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.ejc.2016.05.009 | Eur. J. Comb. |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Minkowski's theorem,Lattice (order),Minkowski space,Polytope,Lattice (group),Integer lattice,Unimodular matrix,Minkowski addition,Mathematics | Journal | 58 |
Issue | ISSN | Citations |
C | 0195-6698 | 0 |
PageRank | References | Authors |
0.34 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ivan Soprunov | 1 | 21 | 3.68 |
| Jenya Soprunova | 2 | 21 | 2.37 |