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
Funding Information: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.
Funding Information:
∗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.
Publisher Copyright:
© 2019 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
Keywords
- Graphs
- Indecomposable matrices
- Permanent