# Pattern avoidance in labelled trees

@article{Dotsenko2011PatternAI, title={Pattern avoidance in labelled trees}, author={Vladimir Dotsenko}, journal={arXiv: Combinatorics}, year={2011} }

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…

## 14 Citations

Noncontiguous Pattern Containment in Binary Trees

- Computer Science, Mathematics
- 2014

This work gives a functional equation for the multivariate generating function for number of -leaf trees containing a specified number of copies of any path tree, and analyzes tree patterns with at most 4 leaves with implications for pattern containment in permutations.

A survey of consecutive patterns in permutations

- Mathematics
- 2016

A consecutive pattern in a permutation π is another permutation \(\sigma\) determined by the relative order of a subsequence of contiguous entries of π. Traditional notions such as descents, runs,…

Block patterns in Stirling permutations

- Mathematics, Computer Science
- 2014

A general result is proved which allows us to compute generating functions for the occurrences of various block patterns in terms of generating functions in permutations, which yields a number of applications involving Wilf equivalence of block patterns and a new interpretation of Bessel polynomials.

Enumeration of polyominoes defined in terms of pattern avoidance or convexity constraints. (Énumération de polyominos définis en terme d'évitement de motif ou de contraintes de convexité)

- Mathematics
- 2014

This thesis considers the problem of characterising and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment, and introduces the concept of pattern avoidance in the context of matrices, more precisely permutation matrices andpolyomino matrices.

Wilf Classes of Non-symmetric Operads

- MathematicsISSAC
- 2021

It is shown that if an operad has a finite Groebner basis, then the monomial basis of the operad forms an unambiguous context-free language.

A family of symmetric functions associated with Stirling permutations

- MathematicsJournal of Combinatorics
- 2019

We present exponential generating function analogues to two classical identities involving the ordinary generating function of the complete homogeneous symmetric functions. After a suitable…

Growth in Varieties of Multioperator Algebras and Groebner Bases in Operads

- MathematicsISSAC
- 2017

It is shown that in general there does not exist an algorithm to decide whether the growth exponent of the codimension sequence of the variety defined by given finite sets of operations and identities is equal to a given rational number.

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