Geodesic
Some simple varieties of trees arising in permutation analysis
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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After extending classical results on simple varieties of trees to trees counted by their number of leaves, we describe a filtration of the set of permutations based on their strong interval trees. For each subclass we provide asymptotic formulas for number of trees (by leaves), average number of nodes of fixed arity, average subtree size sum, and average number of internal nodes. The filtration is motivated by genome comparison of related species. 
@article{DMTCS_2013_special_264_a30,
     author = {Bouvel, Mathilde and Mishna, Marni and Nicaud, Cyril},
     title = {Some simple varieties of trees arising in permutation analysis},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.2346},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2346/}
}
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Bouvel, Mathilde; Mishna, Marni; Nicaud, Cyril. Some simple varieties of trees arising in permutation analysis. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.2346. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2346/

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