Add to ORKGWe 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
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
AbstractIn this paper, we prove a conjecture proposed by Leo: a large minimally 3-connected matroid ...
A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notio...
AbstractWe give several results about the asymptotic behaviour of matroids. Specifically, almost all...
For a matroid M of rank r on n elements, let b(M) denote the fraction of bases of M among the subset...
AbstractVery little is known about the asymptotic behavior of classes of matroids. We make a number ...
Quirk and Seymour have shown that a connected simple graph has at least as many spanning trees as ci...
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that~s(n)∼m(...
This paper proves several extremal results for 3-connected matroids. In particular, it is shown that...
AbstractIt has been conjectured that, asymptotically, almost all matroids are sparse paving matroids...
This paper proves that, for every integernexceeding two, there is a numberN(n) such that every 3-con...
t has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enu...
AbstractThis paper proves several extremal results for 3-connected matroids. In particular, it is sh...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
AbstractIn this paper, we prove a conjecture proposed by Leo: a large minimally 3-connected matroid ...
A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notio...
AbstractWe give several results about the asymptotic behaviour of matroids. Specifically, almost all...
For a matroid M of rank r on n elements, let b(M) denote the fraction of bases of M among the subset...
AbstractVery little is known about the asymptotic behavior of classes of matroids. We make a number ...
Quirk and Seymour have shown that a connected simple graph has at least as many spanning trees as ci...
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that~s(n)∼m(...
This paper proves several extremal results for 3-connected matroids. In particular, it is shown that...
AbstractIt has been conjectured that, asymptotically, almost all matroids are sparse paving matroids...
This paper proves that, for every integernexceeding two, there is a numberN(n) such that every 3-con...
t has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enu...
AbstractThis paper proves several extremal results for 3-connected matroids. In particular, it is sh...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
AbstractIn this paper, we prove a conjecture proposed by Leo: a large minimally 3-connected matroid ...
A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notio...