The partial-fractions method for counting solutions to integral linear systems
| dc.creator | Beck, Matthias | |
| dc.date | 2003-09-19 | |
| dc.date | 2005-01-02 | |
| dc.date.accessioned | 2026-07-07T05:01:19Z | |
| dc.date.available | 2026-07-07T05:01:19Z | |
| dc.description | We present a new tool to compute the number $ϕ_\A (\b)$ of integer solutions to the linear system $$ \x \geq 0 \qquad \A \x = \b $$ where the coefficients of $\A$ and $\b$ are integral. $ϕ_\A (\b)$ is often described as a \emph{vector partition function}. Our methods use partial fraction expansions of Euler's generating function for $ϕ_\A (\b)$. A special class of vector partition functions are Ehrhart (quasi-)polynomials counting integer points in dilated polytopes. | |
| dc.description | 9 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0309332 | |
| dc.identifier | http://arxiv.org/abs/math/0309332 | |
| dc.identifier | Discrete & Computational Geometry 32 (2004), 437-446 (special issue in honor of Louis Billera) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68625 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 52C07; 52C45 | |
| dc.title | The partial-fractions method for counting solutions to integral linear systems | |
| dc.type | text |