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. In addition, we enumerate binary trees that simultaneously avoid more
than one tree pattern. Finally, we explore connections between pattern-avoiding
trees and pattern-avoiding permutations.Comment: 21 pages, 2 figures, 1 tabl
