Pattern Avoidance in Ternary Trees

Nathan Gabriel, Katherine Peske, Lara Pudwell, Samuel Tay
2012 23 11 Article 12.1.5 Journal of Integer Sequences   unpublished
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
more » ... f tree patterns yield the same avoidance generating function. Finally, we compare our bijections to