Abstract
A Latin square of order n is a square matrix with n different numberssuch that numbers in each column and each row are distinct. Max-plus Algebra isalgebra that uses two operations, ⊕ and ⊗. In this paper, we solve the eigenproblemfor Latin squares in Max-plus Algebra by considering the permutations determinedby the numbers in the Latin squares.DOI : http://dx.doi.org/10.22342/jims.20.1.178.37-45
Highlights
IntroductionThe purpose of this paper is to solve eigenproblems in max-plus algebra for Latin squares by considering the permutations of symbol (or numbers) in Latin squares
From a square matrix A, eigenproblems are the problems of finding a scalar λ and corresponding vector v that satisfy Av = λv and we apply this problems into max-plus algebra
Methods to solve eigenproblems in max-plus algebra were handled by several authors for ordinary matrices [6, 7, 8], as well as for special matrices such as circulant matrix [10, 11], Monge matrix [2] and inverse Monge matrix [4]
Summary
The purpose of this paper is to solve eigenproblems in max-plus algebra for Latin squares by considering the permutations of symbol (or numbers) in Latin squares. A reason for studying eigenproblems of Latin square in max-plus algebra is. Syifa’ul and Subiono that such problems have been studied for other matrices, for example Monge matrix [2], inverse Monge matrix [4] and circulant matrix [10, 11].
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