The notion of tree-shifts constitutes an intermediate class in between one-sided shift spaces and multidimensional ones. This paper proposes an algorithm for computing of the entropy of a tree-shift of finite type. Meanwhile, the entropy of a tree-shift of finite type is $\dfrac{1}{p} \ln \lambda$ for some $p \in \mathbb{N}$, where $\lambda$ is a Perron number. This extends Lind's work on one-dimensional shifts of finite type. As an application, the entropy minimality problem is investigated, and we obtain the necessary and sufficient condition for a tree-shift of finite type being entropy minimal with some additional conditions.

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Cayley 树上有限类型位移的熵表征

树移位的概念构成了单边移位空间和多维移位空间之间的中间类。本文提出了一种计算有限类型树移位的熵的算法。同时，对于某些 $p \in \mathbb{N}$，有限类型的树移位的熵是 $\dfrac{1}{p} \ln \lambda$，其中 $\lambda$ 是 Perron 数。这扩展了 Lind 在有限类型的一维移位方面的工作。作为一个应用，研究了熵极小问题，并获得了有限类型树移为熵极小的充要条件，并附加了一些附加条件。