The number of matroids on a finite set
| dc.creator | Dukes, W. M. B. | |
| dc.date | 2004-11-24 | |
| dc.date | 2004-12-13 | |
| dc.date.accessioned | 2026-07-07T05:14:41Z | |
| dc.date.available | 2026-07-07T05:14:41Z | |
| dc.description | In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to be log-convex. We give a recursion for a new, slightly improved, lower bound on the number of rank-$r$ matroids on $n$ elements when $n=2^m-1$. We also prove an adjacent result showing the point-lines-planes conjecture to be true if and only if it is true for a special subcollection of matroids. Two new tables are also presented, giving the number of paving matroids on at most eight elements. | |
| dc.description | 10 pages; revised proofs and corrected typos | |
| dc.identifier | https://arxiv.org/abs/math/0411557 | |
| dc.identifier | http://arxiv.org/abs/math/0411557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73367 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B35 | |
| dc.title | The number of matroids on a finite set | |
| dc.type | text |