In his 2008 thesis [16] , Tateno claimed a counterexample to the Bonato–Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno’s unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides partial orders with a similar conclusion. At the same time these examples also disprove conjectures by Thomassé and Tyomkyn.

中文翻译：

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Tateno 反驳 Bonato-Tardif、Thomase 和 Tyomkyn 猜想的例子

在他 2008 年的论文 [16] 中，Tateno 提出了一个关于树的同态类数量的 Bonato-Tardif 猜想的反例。在本文中，我们重新审视 Tateno 未发表的想法，以提供严格的阐述，构造具有任意有限数量的同态类的局部有限树；改编为偏序提供了类似的结论。同时这些例子也反驳了Thomassé和Tyomkyn的猜想。