  In this paper we propose a notion of pattern avoidance in binary trees that
generalizes the avoidance of contiguous tree patterns studied by Rowland and
non-contiguous tree patterns studied by Dairyko, Pudwell, Tyner, and Wynn.
Specifically, we propose algorithms for generating different classes of binary
trees that are characterized by avoiding one or more of these generalized
patterns. This is achieved by applying the recent
Hartung-Hoang-M\"utze-Williams generation framework, by encoding binary trees
via permutations. In particular, we establish a one-to-one correspondence
between tree patterns and certain mesh permutation patterns. We also conduct a
systematic investigation of all tree patterns on at most 5 vertices, and we
establish bijections between pattern-avoiding binary trees and other
combinatorial objects, in particular pattern-avoiding lattice paths and set
partitions.

Discrete Mathematics;Combinatorics