• Corpus ID: 15145564

# Pattern avoidance in labelled trees

@article{Dotsenko2011PatternAI,
title={Pattern avoidance in labelled trees},
journal={arXiv: Combinatorics},
year={2011}
}
• V. Dotsenko
• Published 4 October 2011
• Mathematics
• arXiv: Combinatorics
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…
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## References

SHOWING 1-10 OF 56 REFERENCES
Pattern avoidance in binary trees
• E. Rowland
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 2010
Generalized Pattern Avoidance
A complete solution is given for the number of permutations avoiding any single pattern of length three with exactly one adjacent pair of letters, and a new class of set partitions is defined, called monotone partitions, and these partitions are in one-to-one correspondence with non-overlapping partitions.
Computational Approaches to Consecutive Pattern Avoidance in Permutations
In recent years, there has been increasing interest in consecutive pattern avoidance in permutations. In this paper, we introduce two approaches to counting permutations that avoid a set of
Using Homological Duality in Consecutive Pattern Avoidance
• Mathematics, Computer Science
Electron. J. Comb.
• 2011
Using an approach suggested by Dotsenko and Khoroshkin we present a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions
A Spectral Approach to Consecutive Pattern-Avoiding Permutations
• Mathematics
• 2010
We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to
Permutations and words counted by consecutive patterns
• Mathematics, Computer Science