Title

ON RANDOM REPRESENTABLE MATROIDS.

Document Type

Article

Publication Date

1-1-1984

Abstract

Results are obtained on the likely connectivity properties and sizes of circuits in the column dependence matroid of a random r multiplied by n matrix over a finite field, for large r and n. In a sense made precise in the paper, it is shown to be highly probable that when n is less than r such a matroid is the free matroid on n points, while if n exceeds r it is a connected matroid of rank r. Moreover, the connectivity can be strengthened under additional hypotheses on the growth of n and r, using the notion of vertical connectivity; and the values of k for which circuits of size k exist can be determined in terms of n and r.

Publication Source (Journal or Book title)

Studies in Applied Mathematics

First Page

181

Last Page

205

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