A Question of Erdős on Doubly Stochastic Matrices [r-libre/4013]

Bouthat, Ludovick; Mashreghi, Javad et Morneau-Guérin, Frédéric (mai 2025). A Question of Erdős on Doubly Stochastic Matrices. Communication (sur invitation) présentée au Canadian Discrete and Algorithmic Mathematics Conference, Ottawa, Canada.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Oui
Étape de publication :	Non publié
Résumé :	In a celebrated paper of Marcus and Ree (1959), it was shown that if A=[a_{ij}] is an n times n doubly stochastic matrix, then there is a permutation sigma in S_n such that sum_{i,j=1}^{n} a_{i,j}^{2} is less than or equal to \sum_{i=1}^{n} a_{i,\sigma(i)}. Erdős asked for which doubly stochastic matrices the inequality is saturated. Although Marcus and Ree provided some insight for the set of solutions, the question appears to have fallen into oblivion. Our goal in this presentation is to present the recent, fast-growing progress on this problem more than 60 years after first being proposed.
Adresse de la version officielle :	https://canadam.ca/2025fr
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	02 mars 2026 18:20
Dernière modification :	02 mars 2026 18:20

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