Elimination of variables and the determinant of the max plus algebra
type: Item
instance of: scholarly article
title: Elimination of variables and the determinant of the max plus algebra
zbMATH Open document ID: 1248.15024
DOI: 10.1088/1751-8113/45/10/105202
published in: Journal of Physics A: Mathematical and Theoretical
publication date: 2012-04-13T00:00:00Z
Mathematics Subject Classification ID: 15A80
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 6023846
zbMATH Keywords: max plus algebra
zbMATH Keywords: determinant
zbMATH Keywords: convex polyhedra
zbMATH Keywords: consistency conditions
zbMATH Keywords: ultradiscrete permanent
zbMATH Keywords: max plus linear equations
zbMATH Keywords: inequality systems
author: N. Shinzawa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1088/1751-8113/45/10/105202
OpenAlex ID: W2013114000
review text: The author develops the idea of the variable elimination described by \textit{N. Shinzawa} and \textit{R. Hirota} [J. Phys. A, Math. Gen. 36, No. 16, 4667--4675 (2003; Zbl 1052.37056)] to give a theoretical foundation for the determinant of the max plus algebra. A special class of max plus linear equations is considered. The max plus linear equations contain the inequality systems as a special case which correspond to the convex polyhedra. As a result, the consistency condition of the corresponding max plus linear equations is obtained. Thereafter, a new type of the determinant as a consistency condition of the class of max plus linear equations is proposed. Some examples of the determinant and the relationship between the ultradiscrete permanent are also shown.
reviewed by: Ctirad Matonoha
description: scientific article; zbMATH DE number 6023846