A Closer Look at Lattice Points in Rational Simplices
| dc.creator | Beck, Matthias | |
| dc.date | 2003-06-02 | |
| dc.date.accessioned | 2026-07-07T04:58:29Z | |
| dc.date.available | 2026-07-07T04:58:29Z | |
| dc.description | We generalize Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n+1 rational vertices, we use its description as the intersection of n+1 halfspaces, which determine the facets of the simplex. Instead of just a single dilation factor, we allow different dilation factors for each of these facets. We give an elementary proof that the lattice point counts in the interior and closure of such a "vector-dilated" simplex are quasipolynomials satisfying an Ehrhart-type reciprocity law. This generalizes the classical reciprocity law for rational polytopes. As an example, we derive a lattice point count formula for a rectangular rational triangle, which enables us to compute the number of lattice points inside any rational polygon. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306034 | |
| dc.identifier | http://arxiv.org/abs/math/0306034 | |
| dc.identifier | Electronic J. Comb. 6, no. 1 (1999), R 37 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67659 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 11D75 | |
| dc.title | A Closer Look at Lattice Points in Rational Simplices | |
| dc.type | text |