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Bouthat, Ludovick; Mashreghi, Javad, & MorneauGuérin, Frédéric (In Press). On a question of Erdős on doubly stochastic matrices. Linear and Multilinear Algebra.
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 OnAQuestionOfErdos.pdf
Content : Accepted Version Restricted access till end January 2024. 

Item Type:  Journal Articles 

Refereed:  Yes 
Status:  In Press 
Abstract:  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 such that the sum sum of the absolute squares of its elements is less or equal to the sum from i=1 to n of a_{i,\sigma(i)}. Erdös 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 is to provide a complete answer in the particular, yet nontrivial, case when n=3. 
Depositor:  MorneauGuérin, Frédéric 
Owner / Manager:  Frédéric MorneauGuérin 
Deposited:  30 May 2023 17:48 
Last Modified:  13 Sep 2023 12:43 
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