skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A Generalization of the Theorem on Forming a Matroid from Parts

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.

Authors:
;  [1];  [2]
  1. St.Petersburg State University, Department of Mathematics and Mechanics (Russian Federation)
  2. Mozhaisky Military Space Academy (Russian Federation)
Publication Date:
OSTI Identifier:
22773918
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; MATHEMATICAL SOLUTIONS; MATRICES

Citation Formats

Lebedinskaya, N. A., E-mail: n.lebedinskaya@spbu.ru, Lebedinskiǐ, D. M., E-mail: d.lebedinsky@spbu.ru, and Smirnov, A. A., E-mail: alexandr.alexandrovich.smirnov@gmail.com. A Generalization of the Theorem on Forming a Matroid from Parts. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3919-5.
Lebedinskaya, N. A., E-mail: n.lebedinskaya@spbu.ru, Lebedinskiǐ, D. M., E-mail: d.lebedinsky@spbu.ru, & Smirnov, A. A., E-mail: alexandr.alexandrovich.smirnov@gmail.com. A Generalization of the Theorem on Forming a Matroid from Parts. United States. doi:10.1007/S10958-018-3919-5.
Lebedinskaya, N. A., E-mail: n.lebedinskaya@spbu.ru, Lebedinskiǐ, D. M., E-mail: d.lebedinsky@spbu.ru, and Smirnov, A. A., E-mail: alexandr.alexandrovich.smirnov@gmail.com. Wed . "A Generalization of the Theorem on Forming a Matroid from Parts". United States. doi:10.1007/S10958-018-3919-5.
@article{osti_22773918,
title = {A Generalization of the Theorem on Forming a Matroid from Parts},
author = {Lebedinskaya, N. A., E-mail: n.lebedinskaya@spbu.ru and Lebedinskiǐ, D. M., E-mail: d.lebedinsky@spbu.ru and Smirnov, A. A., E-mail: alexandr.alexandrovich.smirnov@gmail.com},
abstractNote = {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.},
doi = {10.1007/S10958-018-3919-5},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 6,
volume = 232,
place = {United States},
year = {2018},
month = {8}
}