Mutation effects in ordered trees

TL;DR

This paper studies how mutations in ordered trees affect their structure, providing generating functions for various mutation types and revealing new combinatorial sequences and interpretations.

Contribution

It introduces a comprehensive analysis of mutations in ordered trees, deriving generating functions and uncovering new combinatorial sequences and interpretations.

Findings

Derived generating functions for mutated ordered trees

Identified new combinatorial sequences and interpretations

Provided new insights into mutation effects on tree structures

Abstract

A mutation will affect an individual and some or all of its descendants. In this paper, we investigate ordered trees with a distinguished vertex called the mutator. We describe various mutations in ordered trees, and find the generating functions for statistics concerning trees with those mutations. The examples give new interpretations to several known sequences and also introduce many new sequences and their combinatorial interpretations.