Asymptotic bounds on the numbers of vertices of polytopes of polystochastic matrices
| Autor: | Potapov, Vladimir N., Taranenko, Anna A. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Omega_n^d$. In the present paper, we compare known bounds on the number of vertices of the polytope $\Omega_n^d$ and prove that the number of vertices of $\Omega_3^d$ is doubly exponential on $d$. Comment: 8 pages, Section 2 is transferred from arXiv:2311.06905 |
| Databáze: | arXiv |
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