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Multidimensional permanents in enumeration problems
Authors:S. V. Avgustinovich
Affiliation:(1) Department of Pediatrics, Faculty of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 112-8688 Tokyo, Japan;(2) Department of Internal Medicine, Faculty of Medicine, The University of Tokyo, Tokyo, Japan;(3) McKusick-Nathans Institute for Genetic Medicine, Johns Hopkins Medical Center, Baltimore, USA;(4) Department of Physiology, Faculty of Medicine, Kitasato University, Kanagawa, Japan;(5) Department of Haemodialysis and Apheresis, Faculty of Medicine, The University of Tokyo, Tokyo, Japan;(6) Department of Anatomy, Kyorin University School of Medicine, Tokyo, Japan;(7) Department of Genetics, Mitsubishi Yuka Bio-clinical Laboratories Inc., Tokyo, Japan;(8) Department of Pharmacology and Toxicology, Kyorin University School of Medicine, Tokyo, Japan
Abstract:Permanents are an effective tool for solving many combinatorial problems about enumeration. The respective theory is well developed and has numerous applications. In this paper the problem of counting the number of distinct 1-perfect binary codes is reduced to computing a generalized permanent of a particularly constructed multidimensional matrix.
Keywords:
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