Multidimensional Ehrhart Reciprocity
| dc.creator | Beck, Matthias | |
| dc.date | 2001-11-30 | |
| dc.date | 2003-06-03 | |
| dc.date.accessioned | 2026-07-07T04:44:54Z | |
| dc.date.available | 2026-07-07T04:44:54Z | |
| dc.description | In a previous paper (El. J. Combin. 6 (1999), R37), the author generalized Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational polytope, that is, a polytope with rational vertices, we use its description as the intersection of halfspaces, which determine the facets of the polytope. Instead of just a single dilation factor, we allow different dilation factors for each of these facets. We proved that, if our polytope is a simplex, 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. In the present paper we complete the picture by extending this result to general rational polytopes. As a corollary, we also generalize a reciprocity theorem of Stanley. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111331 | |
| dc.identifier | http://arxiv.org/abs/math/0111331 | |
| dc.identifier | J. Combin. Th. Ser. A 97, no. 1 (2002), 187-194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62783 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 11D75 | |
| dc.title | Multidimensional Ehrhart Reciprocity | |
| dc.type | text |