An analogue of topological sequence entropy for Markov hom tree-shifts

In this article, an analogue h^S_top of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of h^S_top, including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero h^S_top for any S), and the upper bound as well as denseness of all possible values. The relationship between this quantity and a variant called induced entropy is also breifly discussed.