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

Bouthat, Ludovick; Mashreghi, Javad, & Morneau-Guérin, Frédéric (May 2025). A Question of Erdős on Doubly Stochastic Matrices. Paper (invited) presented at the Canadian Discrete and Algorithmic Mathematics Conference, Ottawa, Canada.

File(s) available for this item:

PDF - Présentation_Beamer__CanaDAM_2025_.pdf
Content : Slideshow

Download

Item Type:	Conference papers (unpublished)
Refereed:	Yes
Status:	Unpublished
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 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.
Official URL:	https://canadam.ca/2025fr
Depositor:	Morneau-Guérin, Frédéric
Owner / Manager:	Frédéric Morneau-Guérin
Deposited:	02 Mar 2026 18:20
Last Modified:	02 Mar 2026 18:20

Actions (login required)

RÉVISER