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Brauer and partition diagram models for phylogenetic trees and forests


Francis, A and Jarvis, PD, Brauer and partition diagram models for phylogenetic trees and forests, Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 478, (2262) pp. 1-25. ISSN 1364-5021 (2022) [Refereed Article]

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© 2022. The Authors. This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License, (, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

DOI: doi:10.1098/rspa.2022.0044


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.

Item Details

Item Type:Refereed Article
Keywords:phylogenetics, Brauer diagram, sandwich semigroup, partition monoid
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Biological mathematics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the biological sciences
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:151618
Year Published:2022
Deposited By:Mathematics
Deposited On:2022-08-02
Last Modified:2023-01-10
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