Permanents, max algebra and optimal assignment
type: Item
instance of: scholarly article
title: Permanents, max algebra and optimal assignment
zbMATH Open document ID: 0833.15008
DOI: 10.1016/0024-3795(95)00304-A
author: R. B. Bapat
published in: Linear Algebra and its Applications
publication date: 1995-11-09T00:00:00Z
review text: The max algebra consists of the set \({\mathcal M}= \mathbb{R} \cup \{-\infty\}\) equipped with two binary operations, \(a \oplus b = \max (a,b)\) (addition in \(\mathcal M\)) and \(a \otimes b = a + b\) (multiplication in \(\mathcal M\)). For a square matrix, its permanent over \(({\mathcal M}, \oplus, \otimes)\) is simply the maximum diagonal sum of the matrix. Several results are proved for the permanent over the max algebra \(\mathcal M\), which are analogues of classical results for the permanent of a nonnegative matrix.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 803730
zbMATH Keywords: optimal assignment
zbMATH Keywords: max algebra
zbMATH Keywords: permanent
zbMATH Keywords: nonnegative matrix
reviewed by: Witold Więsław
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 803730