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-leaf tree patterns for any positive integer k. In addition, we give a bijection between between certain sets of pattern-avoiding trees and sets of pattern-avoiding permutations. Finally, we enumerate binary trees that simultaneously avoid more than one tree pattern.
@article{10_37236_2099,
author = {Michael Dairyko and Lara Pudwell and Samantha Tyner and Casey Wynn},
title = {Non-contiguous pattern avoidance in binary trees},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2099},
zbl = {1252.05086},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2099/}
}
TY - JOUR
AU - Michael Dairyko
AU - Lara Pudwell
AU - Samantha Tyner
AU - Casey Wynn
TI - Non-contiguous pattern avoidance in binary trees
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2099/
DO - 10.37236/2099
ID - 10_37236_2099
ER -
%0 Journal Article
%A Michael Dairyko
%A Lara Pudwell
%A Samantha Tyner
%A Casey Wynn
%T Non-contiguous pattern avoidance in binary trees
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2099/
%R 10.37236/2099
%F 10_37236_2099
Michael Dairyko; Lara Pudwell; Samantha Tyner; Casey Wynn. Non-contiguous pattern avoidance in binary trees. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2099
