Geodesic
Some families of trees arising in permutation analysis
Mathilde Bouvel1 ; Marni Mishna2 ; Cyril Nicaud3
1LaBRI/CNRS, Université Bordeaux, and Institut für Mathematik, Universität Zürich
2Dept. Mathematics, Simon Fraser University
3Laboratoire d’Informatique Gaspard Monge (LIGM), Université Paris-Est, Marne-la-Vallée
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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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.
DOI : 10.37236/6504
Classification : 05A15, 05A16, 05C75, 05C05, 05C30
Mots-clés : strong interval trees, separable permutations

Mathilde Bouvel  1   ; Marni Mishna  2   ; Cyril Nicaud  3

1 LaBRI/CNRS, Université Bordeaux, and Institut für Mathematik, Universität Zürich
2 Dept. Mathematics, Simon Fraser University
3 Laboratoire d’Informatique Gaspard Monge (LIGM), Université Paris-Est, Marne-la-Vallée 
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     year = {2020},
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     number = {2},
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Mathilde Bouvel; Marni Mishna; Cyril Nicaud. Some families of trees arising in permutation analysis. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/6504

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