Brauer and partition diagram models for phylogenetic trees and forests

TL;DR

This paper introduces a novel mathematical framework linking phylogenetic trees to Brauer diagrams, enabling new algebraic structures and extending the correspondence to non-binary trees and forests, with potential applications in evolutionary biology.

Contribution

It establishes a new correspondence between phylogenetic trees and Brauer diagrams, extending previous work to include non-binary trees and forests, and explores associated semigroup structures.

Findings

Phylogenetic trees correspond to Brauer diagrams.

Extended the correspondence to non-binary trees and forests.

Set of all forests bijects with partitions of finite sets.

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.