## Factoring higher-dimensional shifts of finite type onto the full shift

AIMEE JOHNSON a1 and KATHLEEN MADDEN a2
a1 Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA 19081, USA (e-mail: aimee@swarthmore.edu)
a2 Department of Mathematics and Computer Science, Drew University, Madison, NJ 07940, USA (e-mail: kmadden@drew.edu)

A one-dimensional shift of finite type $(X, \mathbb Z)$ with entropy at least log n factors onto the full n-shift. The factor map is constructed by exploiting the fact that X, or a subshift of X, is conjugate to a shift of finite type in which every symbol can be followed by at least n symbols. We will investigate analogous statements for higher-dimensional shifts of finite type. We will also show that for a certain class of mixing higher-dimensional shifts of finite type, sufficient entropy implies that $(X,\mathbb Z^d )$ is finitely equivalent to a shift of finite type that maps onto the full n-shift.