Let S be a nonempty finite set with cardinality m. Let M be a matroid on S with no loops. The covering number of an element x in S is the smallest positive integer k such that x is a coloop of the union of k copies of M. We investigate connections between the structure of M and the values of the covering numbers of elements of S. Applications to the study of the rank partition and generalized matrix functions are presented. (C) 1998 Elsevier Science Inc. [References: 12]
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机译：令S为基数为m的非空有限集。令M为无环上S的拟阵。 S中元素x的覆盖数是最小的正整数k，因此x是M个k副本的并集的同环。我们研究M的结构与S元素的覆盖数值之间的联系。介绍了在秩划分和广义矩阵函数研究中的应用。 （C）1998 Elsevier Science Inc. [参考：12]
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