# Non-Contiguous Pattern Avoidance in Binary Trees

@article{Dairyko2012NonContiguousPA, title={Non-Contiguous Pattern Avoidance in Binary Trees}, author={Michael Dairyko and Lara K. Pudwell and Samantha Tyner and Casey Wynn}, journal={Electron. J. Comb.}, year={2012}, volume={19}, pages={22} }

In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare these results to analogous work for contiguous tree patterns. Next, we give an explicit generating function that counts binary trees avoiding a single non-contiguous tree pattern according to number of leaves and show that there is exactly one Wilf class of k…

## 23 Citations

Noncontiguous Pattern Containment in Binary Trees

- Computer Science, Mathematics
- 2014

This work gives a functional equation for the multivariate generating function for number of -leaf trees containing a specified number of copies of any path tree, and analyzes tree patterns with at most 4 leaves with implications for pattern containment in permutations.

Pattern avoidance in forests of binary shrubs

- MathematicsDiscret. 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.

A Generating Tree for Permutations Avoiding the Pattern 122+3

- MathematicsFundam. Informaticae
- 2018

This paper provides an algorithmic description of a generating tree for these permutations, which is a way to build every object of a given size n + 1 in a unique way by performing local modifications on an object of size n, and leads to a direct bijection between 1 23 4-avoiding permutations and valley-marked Dyck paths.

Unbalanced subtrees in binary rooted ordered and un-ordered trees

- Computer Science, Mathematics
- 2012

The aim of this work is to study particular patterns in these classes of trees, where completely unbalanced subtrees are considered, where unbalancing is measured according to the so-called Colless's index.

Pattern-avoiding Dyck paths

- Mathematics
- 2013

We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment…

Supertrees

- Mathematics, Computer ScienceElectron. J. Comb.
- 2020

Both upper and lower bounds on the minimum possible size of a $k$-supertree are obtained in three cases; in the fourth, the minimum size exactly is determined.

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…

Pattern Avoidance in Task-Precedence Posets

- MathematicsDiscret. 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.

Restricted Binary Strings and Generalized Fibonacci Numbers

- MathematicsAUTOMATA
- 2017

Some interesting relations involving k-generalized Fibonacci numbers between the set of length n binary strings avoiding k of consecutive 0’s and 1’S are provided with some more restriction on the first and last letter, via a simple bijection.

Proofs of Conjectures about Pattern-Avoiding Linear Extensions

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2019

This work first considers pattern avoidance in $k$-ary heaps, and proves some conjectures that Anderson, Egge, Riehl, Ryan, Steinke, and Vaughan made about pattern-avoiding linear extensions of rectangular posets.

## References

SHOWING 1-10 OF 28 REFERENCES

Pattern Avoidance in Ternary Trees

- Computer Science
- 2011

A bijective method to restructure specic tree patterns that give the same generating function, and generalizing this process to a larger class of ternary trees.

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…

Patterns and Pattern-Matching in Trees: An Analysis

- Computer Science, MathematicsInf. Control.
- 1983

Unbalanced subtrees in binary rooted ordered and un-ordered trees

- Computer Science, Mathematics
- 2012

The aim of this work is to study particular patterns in these classes of trees, where completely unbalanced subtrees are considered, where unbalancing is measured according to the so-called Colless's index.

Tree Traversals and Permutations

- Mathematics, Computer Science

This work uses preorder, inorder and postorder traversals of binary trees to establish multiple bijections between binary trees and these words, and shows these operators satisfy a sort of multiplicative cancellation.

Generation of Binary Trees from Ballot Sequences

- Computer ScienceJACM
- 1978

An efficient algorithm for generating and indexing all shapes of n-noded binary trees is described The algorithm is based on a correspondence between binary trees and the class of stack-sortable…

The size of the biggest Caterpillar subtree in binary rooted planar trees

- Computer Science
- 2012

The size of the biggest caterpillar subtree becomes then a new parameter with respect to which the authors find several enumerations in planar rooted binary trees.