A logical implication between two conjectures on matrix permanents
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915421250125824 |
|---|---|
| author | Pioge, Léo Pietrasz, Kamil K. Seron, Benoit Novo, Leonardo Cerf, Nicolas J. |
| author_facet | Pioge, Léo Pietrasz, Kamil K. Seron, Benoit Novo, Leonardo Cerf, Nicolas J. |
| contents | We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a non-trivial link between two seemingly unrelated conditions that a positive semidefinite matrix may fulfill. As a corollary, the classes of matrices that are known to obey the first conjecture are then immediately proven to obey the second one. Conversely, we uncover new counterexamples to the first conjecture by exhibiting a previously unknown type of counterexamples to the second conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A logical implication between two conjectures on matrix permanents Pioge, Léo Pietrasz, Kamil K. Seron, Benoit Novo, Leonardo Cerf, Nicolas J. Rings and Algebras Combinatorics Quantum Physics 15A15, 15A18, 15B48 We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a non-trivial link between two seemingly unrelated conditions that a positive semidefinite matrix may fulfill. As a corollary, the classes of matrices that are known to obey the first conjecture are then immediately proven to obey the second one. Conversely, we uncover new counterexamples to the first conjecture by exhibiting a previously unknown type of counterexamples to the second conjecture. |
| title | A logical implication between two conjectures on matrix permanents |
| topic | Rings and Algebras Combinatorics Quantum Physics 15A15, 15A18, 15B48 |
| url | https://arxiv.org/abs/2508.00111 |