Solvable and algebraic systems on infinite ladder

We consider two solvable models with equal entropy on the infinite ladder graph Z x {1, 2}: the uniform spanning forest (USF), the abelian sandpile (ASM). We show that the symbolic models (abelian sandpile and spanning forest) are equal entropy symbolic covers of a certain algebraic dynamical system. In the past results of this nature have been established for sandpile models on lattices Z(d). But we present a first example in case of spanning trees