Zeta Function for Commuting Matrix Shift of Finite Type

Abstract

In this paper we show two-dimensional shifts of finite type whose transition matrices commutes and such that the entries of their product also consist of 0’s and 1’s. In particular, the form of associated zeta function of the two-dimensional shift was obtained. Unlike in the one-dimensional shifts of finite type; we gather that zeta functions for them have not closed form. This result derived by obtaining a formula for the number of periodic points of the subshift of finite type. This formula is then incorporated in the corresponding zeta function.