The covering number of elements of a matroid and associated transformations Original Research Article

Let S be a nonempty finite set with cardinality m. Let image 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.