All doubly stochastic solutions to $AXA = XAX$ when $A$ is a permutation matrix

RESUMO

In this paper we obtain all doubly-stochastic solutions to the Yang-Baxter-like matrix equation $AXA = XAX$ when $A$ is a permutation matrix. We characterize the permutation solutions, proper doubly stochastic solutions, and we accompany our results with suitable examples.