Vertices of the polytope of polystochastic matrices and product constructions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909063993884672 |
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| author | Taranenko, Anna A. |
| author_facet | Taranenko, Anna A. |
| contents | A multidimensional nonnegative matrix is called polystochastic if the sum of its entries at 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 $V(n,d)$ of vertices of the polytope $Ω_n^d$, propose two constructions of vertices of $Ω_n^d$ based on multidimensional matrix multiplication, and list all vertices of the polytope $Ω_3^4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vertices of the polytope of polystochastic matrices and product constructions Taranenko, Anna A. Combinatorics 05B15, 15B51 A multidimensional nonnegative matrix is called polystochastic if the sum of its entries at 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 $V(n,d)$ of vertices of the polytope $Ω_n^d$, propose two constructions of vertices of $Ω_n^d$ based on multidimensional matrix multiplication, and list all vertices of the polytope $Ω_3^4$. |
| title | Vertices of the polytope of polystochastic matrices and product constructions |
| topic | Combinatorics 05B15, 15B51 |
| url | https://arxiv.org/abs/2311.06905 |