The Statistics and Combinatorics of Increasing Trees and Colored Increasing Trees

Garrett Southwood, Hua Wang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)475-487
Number of pages13
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
Volume123
DOIs
StatePublished - 2024

Scopus Subject Areas

  • General Mathematics

Keywords

  • Analytic Combinatorics
  • Generating Functions
  • Increasing Trees

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