Pattern Avoidance in Ternary Trees

Journal of integer sequences

关键词: Mock theta functions;    theta functions;    Gaussian polynomials;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Waterloo * Department of Computer Science

【 摘 要 】

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.

【 授权许可】

Unknown