Abstract

In this article, an analogue \(h^S_{\rm top}\) of topological sequence entropy is defined for Markov hom tree-shifts. We explore various aspects of \(h^S_{\rm top}\), including the existence of the limit in the definition, its relationship to topological entropy, a full characterization of null systems (with zero \(h^S_{\rm top}\) 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.