Permanents of multidimensional matrices: Properties and applications
- Авторы: Taranenko A.1
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Учреждения:
- Sobolev Institute of Mathematics
- Выпуск: Том 10, № 4 (2016)
- Страницы: 567-604
- Раздел: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212562
- DOI: https://doi.org/10.1134/S1990478916040141
- ID: 212562
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Аннотация
The permanent of a multidimensional matrix is the sum of the products of entries over all diagonals. In this survey, we consider the basic properties of the multidimensional permanent, sufficient conditions for its positivity, available upper bounds, and the specifics of the permanents of polystochasticmatrices.We prove that the number of various combinatorial objects can be expressed via multidimensional permanents. Special attention is paid to the number of 1-factors of uniform hypergraphs and the number of transversals in Latin hypercubes.
Об авторах
A. Taranenko
Sobolev Institute of Mathematics
Автор, ответственный за переписку.
Email: taattg@mail.ru
Россия, pr. Akad. Koptyuga 4, Novosibirsk, 630090