Name
Abstract | ||
|---|---|---|
A minor-closed class of matroids is (strongly) fractal if the number of n-element matroids in the class is dominated by the number of n-element excluded minors. We conjecture that when K is an infinite field, the class of K-representable matroids is strongly fractal. We prove that the class of sparse paving matroids with at most k circuit-hyperplanes is a strongly fractal class when k is at least three. The minor-closure of the class of spikes with at most k circuit-hyperplanes (with k≥5) satisfies a strictly weaker condition: the number of 2t-element matroids in the class is dominated by the number of 2t-element excluded minors. However, there are only finitely many excluded minors with ground sets of odd size. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.aam.2019.101995 | Advances in Applied Mathematics |
Keywords | DocType | Volume |
05B35 | Journal | 126 |
ISSN | Citations | PageRank |
0196-8858 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dillon Mayhew | 1 | 102 | 18.63 |
| Mike Newman | 2 | 0 | 0.34 |
| Geoff Whittle | 3 | 471 | 57.57 |