Pattern avoidance in ternary trees

Citation data:

Journal of Integer Sequences, Vol: 15, Issue: 12.5

Publication Year:
2012
Usage 13
Abstract Views 13
Repository URL:
https://works.bepress.com/lara_pudwell/4; https://scholar.valpo.edu/mcs_fac_pubs/3
Author(s):
Pudwell, Lara K.; Gabriel, Nathan; Peske, Katherine; Tay, Samuel
Tags:
Education
article description
This paper considers the enumeration of ternary trees (i.e., rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree patterns; then, for more complex trees, we compute generating functions by extending a known algorithm for pattern-avoiding binary trees. Next, we present an alternate one-dimensional notation for trees which we use to find bijections that explain why certain pairs of tree patterns yield the same avoidance generating function. Finally, we compare our bijections to known “replacement rules” for binary trees and generalize these bijections to a larger class of trees.