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

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