A bijection between phylogenetic trees and plane oriented recursive trees

TL;DR

This paper establishes a bijection between phylogenetic trees and plane oriented recursive trees, linking two combinatorial structures with similar enumeration properties through novel representations.

Contribution

It introduces a new bijection connecting phylogenetic trees and plane oriented recursive trees using 2-partitions and trapezoidal words, revealing their structural relationship.

Findings

Both tree families are enumerated by double factorials.

A bijection is constructed using 2-partitions and trapezoidal words.

The work bridges nonplanar and planar tree structures.

Abstract

Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the respective representations a 2-partitions and trapezoidal words.