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arXiv · 1901.02982

The isometry group of phylogenetic tree space is $S_n$

Gillian Grindstaff
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Abstract

A phylogenetic tree is an acyclic graph with distinctly labeled leaves, whose internal edges have a positive weight. Given a set of n leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube complex known as phylogenetic tree space, or Billera-Holmes-Vogtmann tree space. In this largely combinatorial paper, we show that the isometry group of this space is the symmetric group on n elements. This fact is relevant to distance-based analyses of phylogenetic tree sets.

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Gillian Grindstaff. 2019-03-31. The isometry group of phylogenetic tree space is $S_n$. https://arxiv.org/abs/1901.02982

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