کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4656766 | 1632982 | 2015 | 22 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Counting matroids in minor-closed classes Counting matroids in minor-closed classes](/preview/png/4656766.png)
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 U2,kU2,k, U3,6U3,6, P6P6, Q6Q6 or R6R6, 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 an M(K4)M(K4)-minor which asymptotically matches the best known lower bound on the number of all matroids, due to Knuth.
Journal: Journal of Combinatorial Theory, Series B - Volume 111, March 2015, Pages 126–147