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arXiv · 2111.15225

Brauer and partition diagram models for phylogenetic trees and forests

Andrew Francis·Peter D Jarvis
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Abstract

We introduce a correspondence between phylogenetic trees and Brauer diagrams, inspired by links between binary trees and matchings described by Diaconis and Holmes (1998). This correspondence gives rise to a range of semigroup structures on the set of phylogenetic trees, and opens the prospect of many applications. We furthermore extend the Diaconis-Holmes correspondence from binary trees to non-binary trees and to forests, showing for instance that the set of all forests is in bijection with the set of partitions of finite sets.

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Andrew Francis, Peter D Jarvis. 2021-11-30. Brauer and partition diagram models for phylogenetic trees and forests. https://doi.org/10.1098/rspa.2022.0044

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