Unbalanced subtrees in binary rooted ordered and un-ordered trees
@article{Disanto2012UnbalancedSI, title={Unbalanced subtrees in binary rooted ordered and un-ordered trees}, author={Filippo Disanto}, journal={arXiv: Combinatorics}, year={2012} }
Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely unbalanced subtrees, where unbalancing is measured according to the so-called Colless's index. The size of the biggest unbalanced subtree becomes then a new parameter with respect to which we find several enumerations.
One Citation
Non-Contiguous Pattern Avoidance in Binary Trees
- Computer ScienceElectron. J. Comb.
- 2012
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.
References
SHOWING 1-6 OF 6 REFERENCES
Non-Contiguous Pattern Avoidance in Binary Trees
- Computer ScienceElectron. J. Comb.
- 2012
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.
Analytic Combinatorics
- Mathematics
- 2009
This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.
The Mean and Variance of the Numbers of r-Pronged Nodes and r-Caterpillars in Yule-Generated Genealogical Trees
- Mathematics
- 2006
Abstract.The Yule model is a frequently-used evolutionary model that can be utilized to generate random genealogical trees. Under this model, using a backwards counting method differing from the…
SEARCHING FOR EVOLUTIONARY PATTERNS IN THE SHAPE OF A PHYLOGENETIC TREE
- BiologyEvolution; international journal of organic evolution
- 1993
Six non‐parametric statistical tests that test for nonrandom patterns of branching in any bifurcating tree are developed and compared under a simple model of biased speciation suggest which of them may be most useful for detecting nonrandom tree shapes.
Average Case Analysis of Algorithms on Sequences
- Computer Science, Economics
- 2001
This book provides a unique overview of the tools and techniques used in average case analysis of algorithms.