Explicit Formula for Counting Lattice Points of Polyhedra
| dc.creator | Lasserre, Jean B. | |
| dc.creator | Zeron, Eduardo S. | |
| dc.date | 2007-02-14 | |
| dc.date.accessioned | 2026-07-07T07:46:52Z | |
| dc.date.available | 2026-07-07T07:46:52Z | |
| dc.description | Given $z\in C^n$ and $A\in Z^{m\times n}$, we consider the problem of evaluating the counting function $h(y;z):=\sum\{z^x : x\in Z^n; Ax=y, x\geq 0\}$. We provide an explicit expression for $h(y;z)$ as well as an algorithm with possibly numerous but very simple calculations. In addition, we exhibit finitely many fixed convex cones, explicitly and exclusively defined by $A$, such that for any $y\in Z^m$, the sum $h(y;z)$ can be obtained by a simple formula involving the evaluation of $\sum z^x$ over the integral points of those cones only. At last, we also provide an alternative (and different) formula from a decomposition of the generating function into simpler rational fractions, easy to invert. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702406 | |
| dc.identifier | http://arxiv.org/abs/math/0702406 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123973 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05A15; 51M20; 90C57 | |
| dc.title | Explicit Formula for Counting Lattice Points of Polyhedra | |
| dc.type | text |