Coincidence of 1- and 2-dimensional entropies
Nigel Burke, John Enns · 2014
We compare the entropy of a 1-dimensional shift space, or constrained system, to that of its 2-dimensional version. In particular we study when these entropies are equal. This leads to the introduction of a class of shifts with periodically varying constraints called interleavings of full shifts. We prove that an irreducible sofic shift has the same entropy in 1 and 2 dimensions if and only if it is of this class. We also explore some consequences in higher dimensions.