Counting tanglegrams with species

TL;DR

This paper applies combinatorial species theory to count various types of unlabeled tanglegrams, extending previous work on their enumeration and addressing new variations such as unordered and unrooted forms.

Contribution

It introduces a species-theoretic approach to count multiple variations of unlabeled tanglegrams, including unordered and unrooted types, advancing combinatorial enumeration methods.

Findings

Derived formulas for counting unlabeled tanglegrams

Extended enumeration to unordered and unrooted tanglegrams

Provided a unified combinatorial framework

Abstract

A tanglegram is a pair of binary trees with the same set of leaves. Unlabeled tanglegrams were counted recently by Billey, Konvalinka, and Matsen, who also proposed the problem of counting several variations of unlabeled tanglegrams (unordered and unrooted tanglegrams). We use the theory of combinatorial species to solve these problems.