# 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}
}
• Published 5 March 2012
• Computer Science
• Electron. J. Comb.
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

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## References

SHOWING 1-10 OF 28 REFERENCES
Pattern avoidance in binary trees
• E. Rowland
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 2010
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
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, Mathematics
Inf. Control.
• 1983
Unbalanced subtrees in binary rooted ordered and un-ordered trees
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.
Stack sortable permutations
• D. Rotem
• Computer Science
Discret. Math.
• 1981
Generation of Binary Trees from Ballot Sequences
• Computer Science
JACM
• 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
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.