Permanents of multidimensional matrices: Properties and applications

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• 作者：A. A. Taranenko
• 关键词：permanent ; multidimensional matrix ; stochastic matrix ; polystochastic matrix ; transversal in a Latin hypercube ; 1 ; factor of a uniform hypergraph
• 刊名：Journal of Applied and Industrial Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：10
• 期：4
• 页码：567-604
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Pleiades Publishing
• ISSN：1990-4797
• 卷排序：10

文摘

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.