Table of Contents
ISRN Combinatorics
Volume 2014, Article ID 316535, 8 pages
http://dx.doi.org/10.1155/2014/316535
Research Article

Noncontiguous Pattern Containment in Binary Trees

1Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, IN 46383, USA
2Department of Mathematics, Grand Valley State University, Allendale, MI 49401, USA
3Department of Mathematics, Troy University, Troy, AL 36082, USA
4Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA

Received 28 January 2014; Accepted 5 March 2014; Published 24 March 2014

Academic Editors: A. Glen and A. P. Godbole

Copyright © 2014 Lara Pudwell et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 of times. We give a functional equation for the multivariate generating function for number of -leaf trees containing a specified number of copies of any path tree, and we analyze tree patterns with at most 4 leaves. The paper concludes with implications for pattern containment in permutations.