# Pattern Avoidance in Ternary Trees

@inproceedings{Gabriel2011PatternAI, title={Pattern Avoidance in Ternary Trees}, author={Nathan Gabriel and Katherine Peske and Lara K. Pudwell and Samuel Tay}, year={2011} }

This paper considers the enumeration of ternary trees (i.e. rooted trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by nding the recurrence relations for several simple ternary trees; then, for more complex trees, we extend a known algorithm for nding the generating function that counts n-leaf binary trees avoiding a given pattern. After investigating bijections between these trees’ avoidance sequences and other common combinatorial objects… Expand

#### 15 Citations

Non-Contiguous Pattern Avoidance in Binary Trees

- Mathematics, Computer Science
- Electron. J. Comb.
- 2012

This paper gives an explicit generating function that counts binary trees avoiding a single non-contiguous tree pattern according to number of leaves and shows that there is exactly one Wilf class of k-leaf tree patterns for any positive integer k. Expand

Noncontiguous Pattern Containment in Binary Trees

- Mathematics
- 2014

We consider the enumeration of binary trees containing noncontiguous binary tree patterns. First, we show that any two -leaf binary trees are contained in the set of all -leaf trees the same number… Expand

Pattern avoidance in labelled trees

- Mathematics
- 2011

We discuss a new notion of pattern avoidance motivated by the operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance… Expand

Tree series and pattern avoidance in syntax trees

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2020

A way, given a set of generators and a setof patterns, to enumerate the trees avoiding this last, is described, built around inclusion-exclusion formulas forming a system of equations on formal power series of trees, and composition operations of trees. Expand

Pattern avoidance in forests of binary shrubs

- Mathematics, Computer Science
- Discret. Math. Theor. Comput. Sci.
- 2016

This work enumerates forests avoiding patterns of length three by using the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate. Expand

Rooted forests that avoid sets of permutations

- Mathematics, Computer Science
- Eur. J. Comb.
- 2019

We say that an unordered rooted labeled forest avoids the pattern $\pi\in\mathcal{S}_n$ if the sequence obtained from the labels along the path from the root to any vertex does not contain a… Expand

Pattern Avoidance in Task-Precedence Posets

- Computer Science, Mathematics
- Discret. Math. Theor. Comput. Sci.
- 2016

An interesting application of this work can be found when task-precedence posets represent warehouse package fulfillment by robots, in which case avoidance of both 231 and 321 ensures the authors never stack two heavier packages on top of a lighter package. Expand

Supertrees

- Mathematics, Computer Science
- Electron. J. Comb.
- 2020

This paper obtains both upper and lower bounds on the minimum possible size of a k-supertree in three cases; in the fourth, the minimum size exactly is determined. Expand

Enumerative properties of restricted words and compositions

- Mathematics
- 2018

In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence… Expand

Pattern Avoidance in kary Heaps

- 2017

In this paper, we consider pattern avoidance in k-ary heaps, where the permutation associated with the heap is found by recording the nodes as they are encountered in a breadth-first search. We… Expand

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We discuss a new notion of pattern avoidance motivated by the operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance… Expand

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