Permanents, max algebra and optimal assignment Original Research Article

The max algebra consists of the set of real numbers together with − ∞, equipped with two binary operations, maximization and addition. For a square matrix, its permanent over the max algebra is simply the maximum diagonal sum of the matrix. Several results are proved for the permanent over the max algebra which are analogs of the corresponding results for the permanent of a nonnegative matrix. These include Alexandroff inequality, Bregmanʹs inequality, Cauchy-Binet formula and a Bebianotype expansion.