  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 studied before: consecutive patterns in
words, permutations, coloured permutations etc. The notion of Wilf equivalence
for patterns in permutations admits a straightforward generalisation for (sets
of) tree patterns; we describe classes for trees with small numbers of leaves,
and give several bijections between trees avoiding pattern sets from the same
class. We also explain a few general results for tree pattern avoidance, both
for the exact and the asymptotic enumeration.
