Characterization of polystochastic matrices of order 4 with zero permanent Full article
| Journal |
Journal of Combinatorial Theory. Series A
ISSN: 0097-3165 , E-ISSN: 1096-0899 |
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| Output data | Year: 2025, Volume: 215, Article number : 106060, Pages count : 23 DOI: 10.1016/j.jcta.2025.106060 | ||||||
| Tags | Polystochastic matrix, Permanent of multidimensional matrix, Bitrade, Unitrade, Multidimensional permutation | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
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
Cite:
Perezhogin A.L.
, Potapov V.N.
, Taranenko A.A.
, Vladimirov S.Y.
Characterization of polystochastic matrices of order 4 with zero permanent
Journal of Combinatorial Theory. Series A. 2025. V.215. 106060 :1-23. DOI: 10.1016/j.jcta.2025.106060 WOS Scopus OpenAlex
Characterization of polystochastic matrices of order 4 with zero permanent
Journal of Combinatorial Theory. Series A. 2025. V.215. 106060 :1-23. DOI: 10.1016/j.jcta.2025.106060 WOS Scopus OpenAlex
Dates:
| Submitted: | Oct 14, 2024 |
| Accepted: | Apr 15, 2025 |
| Published print: | Apr 30, 2025 |
| Published online: | Apr 30, 2025 |
Identifiers:
| Web of science: | WOS:001494095200001 |
| Scopus: | 2-s2.0-105003841097 |
| OpenAlex: | W4410017261 |
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