On properties of almost all matroids

被引：6
|
作者：
Lowrance, Lisa [1 ]
Oxley, James [1 ]
Semple, Charles [2 ]
Welsh, Dominic [3 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Univ Canterbury, Dept Math, Christchurch 1, New Zealand
[3] Univ Oxford, Dept Math, Oxford, England
来源：
ADVANCES IN APPLIED MATHEMATICS | 2013年 / 50卷 / 01期
基金：
美国国家科学基金会;
关键词：
Random matroid; Almost all matroids; 3-Connected matroid; RANDOM SUBSETS;
D O I：
10.1016/j.aam.2011.07.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2012 Elsevier Inc. All rights reserved.
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页码：115 / 124
页数：10
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