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arXiv · 2209.03897

On Infinitely Many Siblings for Locally Finite Trees with Parabolic Embeddings

Davoud Abdi
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Abstract

Parabolic (resp. hyperbolic) self-embeddings of trees are those which do not fix a non-empty finite subtree and preserve precisely one (resp. two) end(s). We prove that a locally finite tree having a parabolic self-embedding is mutually embeddable with infinitely many pairwise non-isomorphic trees, unless the tree is a one-way infinite path. As a result, we conclude that two important properties identified by Bonato-Tardif and Tyomkyn hold for locally finite trees not having any hyperbolic self-embedding.

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Davoud Abdi. 2023-01-03. On Infinitely Many Siblings for Locally Finite Trees with Parabolic Embeddings. https://arxiv.org/abs/2209.03897

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