Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices

Vladimir N. Potapov; Anna A. Taranenko

doi:10.1016/j.disc.2025.114653

paper

Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices

arXiv:2406.14160 · doi:10.1016/j.disc.2025.114653

Abstract

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 $Ω_{n}^{d}$ . In the present paper, we compare known bounds on the number of vertices of the polytope $Ω_{n}^{d}$ and prove that the number of vertices of $Ω_{3}^{d}$ is doubly exponential on $d$ .

8 pages, Section 2 is transferred from arXiv:2311.06905

References in corpus (1)

Asymptotics for the number of n-quasigroups of order 4