Frédéric Morneau-Guérin

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math.MG2023

On the Geometry of the Birkhoff Polytope. II. The Schatten $p$ -norms

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \times n$ doubly stochastic matrices, na…

math.MG2023

On a question of Erdős on doubly stochastic matrices

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

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 $σ \in S_{n}$ such that $\su…

On the Geometry of the Birkhoff Polytope. II. The Schatten p-norms

On a question of Erdős on doubly stochastic matrices

On the Geometry of the Birkhoff Polytope. II. The Schatten $p$ -norms