Pattern avoidance in binary trees

@article{Rowland2010PatternAI,
  title={Pattern avoidance in binary trees},
  author={Eric S. Rowland},
  journal={J. Comb. Theory, Ser. A},
  year={2010},
  volume={117},
  pages={741-758}
}
  • E. Rowland
  • Published 2 September 2008
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A

Figures from this paper

Non-Contiguous Pattern Avoidance in Binary Trees
TLDR
This paper gives an explicit generating function that counts binary trees avoiding a single non-contiguous tree pattern according to number of leaves and shows that there is exactly one Wilf class of k-leaf tree patterns for any positive integer k.
Pattern Avoidance in Ternary Trees
TLDR
A bijective method to restructure specic tree patterns that give the same generating function, and generalizing this process to a larger class of ternary trees.
Pattern avoidance in labelled trees
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
Noncontiguous Pattern Containment in Binary Trees
TLDR
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.
Pattern avoidance in forests of binary shrubs
TLDR
This work enumerates forests avoiding patterns of length three by using the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate.
A Generating Tree for Permutations Avoiding the Pattern 122+3
TLDR
This paper provides an algorithmic description of a generating tree for these permutations, which is a way to build every object of a given size n + 1 in a unique way by performing local modifications on an object of size n, and leads to a direct bijection between 1 23 4-avoiding permutations and valley-marked Dyck paths.
Rooted forests that avoid sets of permutations
Unbalanced subtrees in binary rooted ordered and un-ordered trees
TLDR
The aim of this work is to study particular patterns in these classes of trees, where completely unbalanced subtrees are considered, where unbalancing is measured according to the so-called Colless's index.
Block patterns in Stirling permutations
TLDR
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.
Proofs of Conjectures about Pattern-Avoiding Linear Extensions
  • Colin Defant
  • Mathematics
    Discret. Math. Theor. Comput. Sci.
  • 2019
TLDR
This work first considers pattern avoidance in $k$-ary heaps, and proves some conjectures that Anderson, Egge, Riehl, Ryan, Steinke, and Vaughan made about pattern-avoiding linear extensions of rectangular posets.
...
...

References

SHOWING 1-10 OF 22 REFERENCES
Patterns and Pattern-Matching in Trees: An Analysis
Counting strings in Dyck paths
Analytic Variations on the Common Subexpression Problem
TLDR
It is established here that, under a variety of probabilistic models, a tree of size n has a compacted form of expected size asymptotically, where the constant C is explicitly related to the type of trees to be compacted and to the statistical model reflecting tree usage.
What Is Enumerative Combinatorics
The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I
AN INVERSION THEOREM FOR CLUSTER DECOMPOSITIONS OF SEQUENCES WITH DISTINGUISHED SUBSEQUENCES
Certain enumeration problems may be expressed in terms of sequences possessing a specified number of subsequences which are elements of a prescribed set of distinguished sequences. We obtain an
The encyclopedia of integer sequences
TLDR
This book presents methods for Computer Investigation of Sequences, a method for hand analysis of sequences, and some of the methods used in this work, as well as suggestions for further study.
Motzkin Numbers
Enumerative Combinatorics: Volume 1
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of
Dyck path enumeration
...
...