Eventual Regularity of Tropical Semigroup Matrix Powers.

Source abstract

We study regularity of powers of matrices over the tropical semiring. A matrix A\in M_n(\mathbb{T}) is called eventually regular if A^k is regular for some positive integer k. For such a matrix, we define the regularity index \rho(A)=\min{k\geq1}. We establish sufficient conditions for eventual regularity and for regularity to be preserved under tropical matrix powers. We also show that regularity is invariant under finite tropical scalar multiplication and relate this property to the eventual projective periodicity of max-plus matrix powers.