Brauer and partition diagram models for phylogenetic trees and forests
Andrew R. Francis, Peter Jarvis · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2022
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.