Brauer and partition diagram models for phylogenetic trees and forests [article]

Andrew Francis, Peter D Jarvis
2022 arXiv   pre-print
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.
arXiv:2111.15225v3 fatcat:qytk26pz5ze6pno2zp4tq6kjp4