A Generalization of the Theorem on Forming a Matroid from Parts
- Authors: Lebedinskaya N.A.1, Lebedinskiǐ D.M.1, Smirnov A.A.2
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Affiliations:
- Department of Mathematics and Mechanics, St.Petersburg State University
- Mozhaisky Military Space Academy
- Issue: Vol 232, No 6 (2018)
- Pages: 921-925
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241495
- DOI: https://doi.org/10.1007/s10958-018-3919-5
- ID: 241495
Cite item
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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