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On a question of Erdős on doubly stochastic matrices [r-libre/2968]

Bouthat, Ludovick; Mashreghi, Javad, & Morneau-Guérin, Frédéric (2024). On a question of Erdős on doubly stochastic matrices. Linear and Multilinear Algebra. https://doi.org/10.1080/03081087.2023.2300674

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  PDF - OnAQuestionOfErdos.pdf
Content : Accepted Version
Restricted access till end- December 2027.
 
Item Type: Journal Articles
Refereed: Yes
Status: Published
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 non-trivial, case when n=3.
Depositor: Morneau-Guérin, Frédéric
Owner / Manager: Frédéric Morneau-Guérin
Deposited: 30 May 2023 17:48
Last Modified: 12 Jan 2024 19:38

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