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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.

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