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.
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