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The covering number of elements of a matroid and associated transformations

✍ Scribed by Rosário Fernandes

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
141 KB
Volume
298
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let S be a nonempty finite set with cardinality m. Let M = (S, I(M)) be a matroid on S. Let x be an element of S which is not a loop of M. The covering number of x in M is the smallest positive integer s such that x is a coloop of the union of s copies of M. We investigate relations between the covering number of the elements in M and in its minors. Applications to the study of the rank partition and associated transformation are presented.

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