Permanents of multidimensional matrices: Properties and applications
- Autores: Taranenko A.1
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Afiliações:
- Sobolev Institute of Mathematics
- Edição: Volume 10, Nº 4 (2016)
- Páginas: 567-604
- Seção: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212562
- DOI: https://doi.org/10.1134/S1990478916040141
- ID: 212562
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Resumo
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.
Sobre autores
A. Taranenko
Sobolev Institute of Mathematics
Autor responsável pela correspondência
Email: taattg@mail.ru
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