We prove asymptotic upper bounds on the number of paving matroids of fixed rank, using a mixture of entropy counting, sparse encoding, and the probabilistic method
t has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enu... Read more
For a matroid M of rank r on n elements, let b(M) denote the fraction of bases of M among the subset... Read more
A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notio... Read more
We prove asymptotic upper bounds on the number of paving matroids of fixed rank, using a mixture of ... Read more
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that~s(n)∼m(... Read more
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