• Citer

A logical implication between two conjectures on matrix permanents

par Pioge, Léo ;Pietrasz, Kamil;Seron, Benoît ;Goncalves Novo, Leonardo Filipe ;Cerf, Nicolas
Référence Linear algebra and its applications, 725, page (309-318)
Publication Publié, 2025-11

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

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 nontrivial 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. Interestingly, such a relationship between these two mathematical conjectures appears from considerations on their quantum physics implications.