Brauer and partition diagram models for phylogenetic trees and forests

2022/06/01 by Andrew Francis, Peter Jarvis · 1 voice
Computer Science · #Topological and Geometric Data Analysis

paper · doi:10.1098/rspa.2022.0044

openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 Proc. Natl Acad. Sci. USA 95 , 14 600–14 602. ( doi:10.1073/pnas.95.25.14600 )). 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.

Citations

• Cases in which Parsimony or Compatibility Methods will be Positively Misleading

Discussions

• doi.org/10.1098/rspa... We show that sets of phylogenetic trees (that is, forests) are in bijection with all partitions of finite sets! And there are links to partition monoids that we hope will bri [bsky, 2 points, 0 comments]

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