A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each line is equal to $1$. The set of all polystochastic matrices of order n and dimension d is a convex polytope Ωₙᵈ. In the present paper, we compare known bounds on the number of vertices of the polytope Ωₙᵈ and prove that the number of vertices of Ω₃ᵈ is doubly exponential on d.
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Potapov et al. (2024) studied this question.
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