Characterization of polystochastic matrices of order $4$ with zero permanent
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917106754256896 |
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| author | Perezhogin, A. L. Potapov, V. N. Taranenko, A. A. Vladimirov, S. Yu. |
| author_facet | Perezhogin, A. L. Potapov, V. N. Taranenko, A. A. Vladimirov, S. Yu. |
| contents | A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, then the permanent of a $d$-dimensional polystochastic matrix of order $4$ is positive, and for odd $d$, we give a complete characterization of $d$-dimensional polystochastic matrices with zero permanent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of polystochastic matrices of order $4$ with zero permanent Perezhogin, A. L. Potapov, V. N. Taranenko, A. A. Vladimirov, S. Yu. Combinatorics 15B51, 15A15, 05D15, 05B15 A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, then the permanent of a $d$-dimensional polystochastic matrix of order $4$ is positive, and for odd $d$, we give a complete characterization of $d$-dimensional polystochastic matrices with zero permanent. |
| title | Characterization of polystochastic matrices of order $4$ with zero permanent |
| topic | Combinatorics 15B51, 15A15, 05D15, 05B15 |
| url | https://arxiv.org/abs/2410.09546 |