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Doubly stochastic matrices and the Bruhat order

Richard A. Brualdi, Geir Dahl, Eliseu Fritscher (2016)

Czechoslovak Mathematical Journal

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$ which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class $Ω_{n}$ of doubly stochastic matrices (convex hull of $n \times n$ permutation matrices). An alternative description of this partial order is given. We define a class of special faces of $Ω_{n}$ induced by permutation matrices,...

Drei-Nachrichten-Probleme in verallgemeinerter Definition.

Richard Gabriel (1977)

Journal für die reine und angewandte Mathematik

Dualità e teoria dei grafi per la completa positività di matrici

Francesco Barioli (2001)

Bollettino dell'Unione Matematica Italiana

Duality of real and quaternionic random matrices.

Bryc, Wlodek, Pierce, Virgil (2009)

Electronic Journal of Probability [electronic only]

Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

Rawad Abdulghafor, Farruh Shahidi, Akram Zeki, Sherzod Turaev (2016)

Open Mathematics

The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications...