# 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:

- St.Petersburg State University, Department of Mathematics and Mechanics (Russian Federation)
- 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}

}

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