On properties of almost all matroids
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. © 2012 Elsevier Inc.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Lowrance, L., Oxley, J., Semple, C., & Welsh, D. (2013). On properties of almost all matroids. Advances in Applied Mathematics, 50 (1), 115-124. https://doi.org/10.1016/j.aam.2011.07.005