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Some families of trees arising in permutation analysis


Bouvel, Mathilde; Mishna, Marni; Nicaud, Cyril (2020). Some families of trees arising in permutation analysis. Electronic Journal of Combinatorics, 27(2):P2.20.

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.

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.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Theoretical Computer Science
Physical Sciences > Geometry and Topology
Physical Sciences > Discrete Mathematics and Combinatorics
Physical Sciences > Computational Theory and Mathematics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Theoretical Computer Science, Computational Theory and Mathematics, Geometry and Topology
Language:English
Date:15 May 2020
Deposited On:06 Nov 2020 12:25
Last Modified:07 Nov 2020 21:01
Publisher:American Mathematical Society
ISSN:1077-8926
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.37236/6504

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