Computation of Atomic Fibers of Z-Linear Maps
| dc.creator | Hemmecke, Raymond | |
| dc.date | 2004-10-12 | |
| dc.date.accessioned | 2026-07-07T05:13:12Z | |
| dc.date.available | 2026-07-07T05:13:12Z | |
| dc.description | For given matrix $A\in\Z^{d\times n}$, the set $P^I_{A,b}=\{z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P^I_{A,b}$ is called atomic, if $P^I_{A,b}=P^I_{A,b_1}+P^I_{A,b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, application to integer programming, and computational examples are included as well. | |
| dc.identifier | https://arxiv.org/abs/math/0410289 | |
| dc.identifier | http://arxiv.org/abs/math/0410289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72861 | |
| dc.subject | Combinatorics | |
| dc.title | Computation of Atomic Fibers of Z-Linear Maps | |
| dc.type | text |