Counting matroids in minor-closed classes
| Autor: | Pendavingh, R. A., van der Pol, J. G. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Popis: | A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for the complexity of a matroid, and present bounds on the number of matroids on $n$ elements whose cover complexity is bounded. We apply cover complexity to show that the class of matroids without an $N$-minor is asymptotically small in case $N$ is one of the sparse paving matroids $U_{2,k}$, $U_{3,6}$, $P_6$, $Q_6$, or $R_6$, thus confirming a few special cases of a conjecture due to Mayhew, Newman, Welsh, and Whittle. On the other hand, we show a lower bound on the number of matroids without $M(K_4)$-minor which asymptoticaly matches the best known lower bound on the number of all matroids, due to Knuth. 13 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|