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Threshold distribution functions for some random representable matroids

Published online by Cambridge University Press:  24 October 2008

James G. Oxley
James G. Oxley
Affiliation:
Department of Mathematics, IAS, Australian National University, PO Box 4, Canberra, 2600, Australia
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Extract

A random submatroid ωr of the projective geometry PG(r − 1, q) is obtained from PG(r − 1, q) by deleting elements so that each element has, independently of all other elements, probability 1 − p of being deleted and probability p of being retained. The properties of such random structures were studied in [5] and [6]. In the first of these papers, p was kept fixed, while in the second, motivated by Erdös and Rényi's work ([3), [4]) on random graphs, p was taken to be a function of r. A recent paper of Bollobás[2] strengthens and extends a number of the results of Erdös and Rényi. In this paper we prove matroid analogues of several of Bollobàs's results thereby extending some of the results of [6].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 335 - 347
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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