Trivial and Nontrivial Eigenvectors for Latin Squares in Max-Plus Algebra

Abstract

A square array whose all rows and columns are different permutations of the same length over the same symbol set is known as a Latin square. A Latin square may or may not be symmetric. For classification and enumeration purposes, symmetric, non-symmetric, conjugate symmetric, and totally symmetric Latin squares play vital roles. This article discusses the Eigenproblem of non-symmetric Latin squares in well known max-plus algebra. By defining a certain vector corresponding to each cycle of a permutation of the Latin square, we characterize and find the Eigenvalue as well as the possible Eigenvectors.