Abstract
Let A be a (0, 1)-matrix such that PA is indecomposable for every permutation matrix P and there are 2n + 3 positive entries in A. Assume that A is also nonconvertible in a sense that no change of signs of matrix entries, satisfies the condition that the permanent of A equals to the determinant of the changed matrix. We characterized all matrices with the above properties in terms of bipartite graphs. Here 2n + 3 is known to be the smallest integer for which nonconvertible fully indecomposable matrices do exist. So, our result provides the complete characterization of extremal matrices in this class.
| Original language | English |
|---|---|
| Pages (from-to) | 141-151 |
| Number of pages | 11 |
| Journal | Ars Mathematica Contemporanea |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
Funding
The work of the second and the fourth authors was partially supported by Slovenian Research Agency (research core fundings No. P1-0288, No. P1-0222, and by grant BI-RU/16-18-033). The work of the first and the third authors is supported by Russian Scientific Foundation grant 17-11-01124. ∗The work of the second and the fourth authors was partially supported by Slovenian Research Agency (research core fundings No. P1-0288, No. P1-0222, and by grant BI-RU/16-18-033). The work of the first and the third authors is supported by Russian Scientific Foundation grant 17-11-01124.
| Funders | Funder number |
|---|---|
| Russian Scientific Foundation | |
| Javna Agencija za Raziskovalno Dejavnost RS | P1-0222, P1-0288, BI-RU/16-18-033 |
| Russian Science Foundation | 17-11-01124 |
Keywords
- Graphs
- Indecomposable matrices
- Permanent