Invariant measures for bipermutative cellular automata (Q1779048)

This paper continues the investigation of invariant measures for various classes of cellular automata. Here, invariant measures are characterised for cellular automata that depend only on the current cell and the cell immediately to the right under a condition of permutativity on both sides. In particular, it is shown that for any invariant measure the cellular automaton is \(K\)-to-\(1\) almost surely for some fixed \(K\). Applications and examples are given, including situations where positive entropy alone forces the measure to be an algebraic one.