Morneau-Guérin, Frédéric 
ORCID: https://orcid.org/0000-0001-7610-4648
(sous presse).
A nonnegativity criterion for Erdős matrices. Bulletin of the Australian Mathematical Society.
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- erdos_matrices_bams.pdf
Contenu du fichier : Manuscrit accepté (révisé après évaluation) Accès restreint jusqu'à fin- 1 janvier 2027. |
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| Catégorie de document : | Articles de revues |
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| Évaluation par un comité de lecture : | Oui |
| Étape de publication : | Accepté (sous presse) |
| Résumé : | Let A be an n by n doubly stochastic matrix. The Marcus-Ree inequality asserts that the squre of the Frobenius norm of A is less than or equal to the maximal trace of A. Matrices attaining equality are called Erdős matrices. Recent work of Karmakar, Krishna, Pal and Krishna Teja shows that every Erdős matrix is a restricted common diagonal sum matrix. By the structural theory of Brualdi and Dahl, a restricted common diagonal sum matrix with fully indecomposable skeleton S=(s_{ij}) admits additive potentials satisfying a_{ij}=(u_i+v_j)s_{ij}. Karmakar et al.\ observed that the min_i(u_i)+min_j(v_j) is greater or equal to 0 is sufficient for Erdős-ness. We prove that it is also necessary. Thus recognition reduces to solving one linear system per fully indecomposable block and checking signs, with no residual maxtrace computation. |
| Déposant: | Morneau-Guérin, Frédéric |
| Responsable : | Frédéric Morneau-Guérin |
| Dépôt : | 28 aout 2026 13:13 |
| Dernière modification : | 28 aout 2026 13:13 |
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