## 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 |
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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 |
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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