## Projectional Entropy in Higher Dimensional Shifts of Finite Type

**Aimee Johnson***Electronic mail address: aimee@swarthmore.edu**Department of Mathematics and Statistics,**Swarthmore College, Swarthmore, PA 19081*

**Steve Kass***Electronic mail address: skass@drew.edu**Department of Mathematics and Computer Science,**Drew University, Madison, NJ 07940*

**Kathleen Madden***Electronic mail address: kmadden@drew.edu**Department of Mathematics and Computer Science,**Drew University, Madison, NJ 07940*

#### Abstract

Any higher dimensional shift space (*X, ℤ ^{d}*) contains many lower dimensional shift spaces obtained by projection onto

*r*-dimensional sublattices

*L*of

*ℤ*where

^{d}*r < d*. We show here that any projectional entropy is bounded below by the

*ℤ*entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite product of a lower dimensional projection.

^{d}