On properties of almost all matroids |
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| Authors: | Lisa Lowrance James Oxley Charles Semple Dominic Welsh |
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| Institution: | 1. Mathematics Department, Louisiana State University, Baton Rouge, LA, United States;2. Mathematics Department, University of Canterbury, Christchurch, New Zealand;3. Mathematics Department, University of Oxford, Oxford, United Kingdom |
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| Abstract: | We give several results about the asymptotic behaviour of matroids. Specifically, almost all matroids are simple and cosimple and, indeed, are 3-connected. This verifies a strengthening of a conjecture of Mayhew, Newman, Welsh, and Whittle. We prove several quantitative results including giving bounds on the rank, a bound on the number of bases, the number of circuits, and the maximum circuit size of almost all matroids. |
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| Keywords: | 05B35 |
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