Université TÉLUQ

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20102026

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288 citations

Showing 2023 · math.MGShow all

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math.MG2023★ 2 cited

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★ 4 cited

On the Geometry of the Birkhoff Polytope. I. The operator $ℓ_{n}^{p}$ -norms

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n \times n$ doubly stochastic matrices, has been an active subject of research. While its faces, edges a…

math.MG2023★ 4 cited

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 the Geometry of the Birkhoff Polytope. I. The operator ℓnp​-norms

On a question of Erdős on doubly stochastic matrices

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

On the Geometry of the Birkhoff Polytope. I. The operator $ℓ_{n}^{p}$ -norms