Tropical determinant of integer doubly-stochastic matrices

Abstract: Let be the set of all the integer points in the m-dilate of the Birkhoff polytope of doubly-stochastic matrices. In this paper we find the sharp upper bound on the tropical determinant over the set . We define a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find the sharp lower bound on thus defined tropical determinant over . [Copyright &y& Elsevier]