Abstract
In this paper, we prove an analogous to a result of Erdos and Renyi and of Kelly and Oxley. We also show that there are several properties of k-balanced matroids for which there exists a threshold function.
Highlights
If M is a matroid on a set E and X ⊆ E, r(X) will denote the rank of X in M
The k-density of a matroid M with rank greater than k is given by dk (M )
R(M )−k is the size of the ground set of M and r(M) is the rank of the matroid M
Summary
Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International Let M = ( E, F ) denote the matroid on the ground set E with flats F. If M is a matroid on a set E and X ⊆ E, r(X) will denote the rank of X in M. The uniform matroid of rank r and size n is denoted by Ur,n where r = 0,1, , n .
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