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.
- Pub Date:
- October 2011
- Mathematics - Combinatorics;
- Mathematics - Category Theory;
- 05C05 (Primary) 05A15;
- 18D50 (Secondary)
- 27 pages, corrected various misprints, added an appendix explaining the operadic context