Some families of trees arising in permutation analysis
Abstract
We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these results to strong interval trees with a restriction on the arity of prime nodes. Doing so, we describe a filtration of the set of permutations based on their strong interval trees. This filtration is also studied from a purely analytical point of view, thus illustrating the convergence of analytic series towards a non-analytic limit at the level of the asymptotic behavior of their coefficients.
Keywords
Cite
@article{arxiv.1609.09586,
title = {Some families of trees arising in permutation analysis},
author = {Mathilde Bouvel and Marni Mishna and Cyril Nicaud},
journal= {arXiv preprint arXiv:1609.09586},
year = {2016}
}
Comments
26 pages; An extended abstract of this work appeared in the Proceedings of the International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) 2013