A Generalization of the Theorem on Forming a Matroid from Parts


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Abstract

The following generalization of the theorem on forming a matroid from parts is proved: If a finite set is subdivided into some blocks, each of which is supplied with a matroid structure, and the ranks of every union of certain blocks are prescribed and satisfy the conditions on the rank function of a matroid, then the rank function can be extended to all the subsets of the original set in such a way that the latter becomes a matroid.

About the authors

N. A. Lebedinskaya

Department of Mathematics and Mechanics, St.Petersburg State University

Author for correspondence.
Email: n.lebedinskaya@spbu.ru
Russian Federation, St.Petersburg

D. M. Lebedinskiǐ

Department of Mathematics and Mechanics, St.Petersburg State University

Email: n.lebedinskaya@spbu.ru
Russian Federation, St.Petersburg

A. A. Smirnov

Mozhaisky Military Space Academy

Email: n.lebedinskaya@spbu.ru
Russian Federation, St.Petersburg

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