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"Logarithmically" almost all matroids are sparse-paving
Algebra & Discrete Mathematics| Speaker: | Martha Yoko Takane Imay, Universidad Nacional Autonoma de Mexico |
| Location: | 2112 MSB |
| Start time: | Mon, Feb 10 2014, 4:10PM |
In the enumeration of non-isomorphic simple matroids on a set of 9 or less elements, paving matroids predominate. "Does this hold in general?" is a question posed by Blackburn, Crapo and Higgs in [BCH'73]. A weaker conjecture due to Bansal, Pendavingh and van der Pol [BPvP'2012], says: Does lim_n→∞ loglog|Matroid_n| / loglog|Sparse_n| =1 hold? We proved this conjecture, where Matroid_n (respectively, Sparse_n) denotes the set of simple (resp., sparse-paving) matroids on a set of n elements.