Permanents of multidimensional matrices: Properties and applications
- Authors: Taranenko A.A.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 10, No 4 (2016)
- Pages: 567-604
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212562
- DOI: https://doi.org/10.1134/S1990478916040141
- ID: 212562
Cite item
Abstract
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.
About the authors
A. A. Taranenko
Sobolev Institute of Mathematics
Author for correspondence.
Email: taattg@mail.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090