On Stanley's reciprocity theorem for rational cones
| dc.creator | Beck, Matthias | |
| dc.creator | Develin, Mike | |
| dc.date | 2004-09-28 | |
| dc.date | 2005-08-04 | |
| dc.date.accessioned | 2026-07-07T05:12:40Z | |
| dc.date.available | 2026-07-07T05:12:40Z | |
| dc.description | We give a short, self-contained proof of Stanley's reciprocity theorem for a rational cone K \subset R^d. Namely, let sigma_K (x) = sum_{m \in K \cap Z^d} x^m. Then sigma_K (x) and sigma_int(K) (x) are rational functions which satisfy the identity sigma_K (1/x) = (-1)^d sigma_int(K) (x). A corollary of Stanley's theorem is the Ehrhart-Macdonald reciprocity theorem for the lattice-point enumerator of rational polytopes. A distinguishing feature of our proof is that it uses neither the shelling of a polyhedron nor the concept of finite additive measures. The proof follows from elementary techniques in contour integration. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409562 | |
| dc.identifier | http://arxiv.org/abs/math/0409562 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72662 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 52C07 | |
| dc.title | On Stanley's reciprocity theorem for rational cones | |
| dc.type | text |