Honors College Theses

Publication Date

2024

Major

Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Dr. Hua Wang

Abstract

We consider the generating function for increasingly labelled trees. By generalizing the proof through symbolic method, we are able to study various statistics regarding binary increasing trees with respect to height restrictions. We then apply our approach to special colorings of increasing trees in order to obtain their generating functions and, from there, derive the counting sequence for (ak+a)-colored recursive trees. We also present some interesting bijections between colored and non-colored increasing trees.

Thesis Summary

This thesis uses symbolic methods to compute generating functions and statistics for special classes of trees known as increasing trees under certain conditions, such as the case of the increasing trees being of a restricted height or with special colorings applied. We also present some bijections between colored and non-colored increasing trees.

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