On dual of the generalized splitting matroids

Document Type : Research Paper

Authors

Department of Mathematics, Urmia University, Urmia, Iran

Abstract

Given a binary matroid M and a subset TE(M), Luis A. Goddyn posed a problem that the dual of the splitting of M, i.e., ((MT)) is not always equal to the splitting of the dual of M, ((M)T). This persuade us to ask if we can characterize those binary matroids for which (MT)=(M)T. Santosh B. Dhotre answered this question for a two-element subset T. In this paper, we generalize his result for any subset TE(M) and exhibit a criterion for a binary matroid M and subsets T for which (MT) and (M)T are the equal. We also show that there is no subset TE(M) for which, the dual of element splitting of M, i.e., ((MT)) equals to the element splitting of the dual of M, ((M)T).

Keywords


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