An example of Tateno disproving conjectures of Bonato-Tardif, Thomasse, and Tyomkyn
Davoud Abdi, Claude Laflamme, Tateno, Atsushi, Robert E. Woodrow · arXiv (Cornell University) · 2022
In his 2008 thesis, 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 In this paper we revisit Tateno's unpublished ideas to provide a rigorous exposition, constructing locally finite trees having an arbitrary finite number of equimorphy classes; an adaptation provides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 Thomasse and Tyomkyn.