Combinatorial Generation of Matroid Representations: Theory and Practice
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Acta Universitatis Matthiae Belii, Series Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | http://actamath.savbb.sk/ |
| Field | General mathematics |
| Keywords | representable matroid; exhaustive generation |
| Description | Matroids (also called combinatorial geometries) present a strong combinatorial generalization of graphs and matrices. Unlike isomorph-free generation of graphs, which has been extensively studied both from theoretical and practical points of view, not much research has been done so far about matroid generation. Perhaps the main problem with matroid generation lies in a very complex internal structure of a matroid. That is why we focus on generation of suitable matroid representations, and we outline a way how to exhaustively generate matroid representations over finite fields in reasonable computing time. In particular, we extend here some enumeration results on binary (over the binary field) combinatorial geometries by Kingan et al. |
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