Geodesic
Pattern Avoidance in Labelled Trees
Séminaire lotharingien de combinatoire, Tome 67 (2012-2015)

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We discuss a new notion of pattern avoidance motivated by 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 exact and asymptotic enumeration. 

@article{SLC_2012-2015_67_a1,
     author = {Vladimir Dotsenko},
     title = {Pattern {Avoidance} in {Labelled} {Trees}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {67},
     year = {2012-2015},
     url = {http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a1/}
}
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AU  - Vladimir Dotsenko
TI  - Pattern Avoidance in Labelled Trees
JO  - Séminaire lotharingien de combinatoire
PY  - 2012-2015
VL  - 67
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a1/
ID  - SLC_2012-2015_67_a1
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%0 Journal Article
%A Vladimir Dotsenko
%T Pattern Avoidance in Labelled Trees
%J Séminaire lotharingien de combinatoire
%D 2012-2015
%V 67
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a1/
%F SLC_2012-2015_67_a1
Vladimir Dotsenko. Pattern Avoidance in Labelled Trees. Séminaire lotharingien de combinatoire, Tome 67 (2012-2015). http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a1/