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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.09149 |
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Table of Contents:
- A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each of its lines equals $1$. The set of all polystochastic matrices of order $n$ and dimension $d$ is a convex polytope $Ω_n^d$ known as the Birkhoff polytope. In this paper, we identify all vertices of the polytopes $Ω_4^3$ and $Ω_3^4$ correcting the results of Ke, Li, and Xiao (2016). Additionally, we describe constructions vertices of $Ω_n^d$ using multidimensional matrix products and find symmetric vertices of $Ω_3^d$ for all $d \geq 4$ with large support sizes.