Résumé
In this paper1, we generalize 2-trees by replacing triangles by quadrilaterals, pentagons or k-sided polygons (k-gons), where k ≥ 3 is given. This generalization, to k-gonal 2-trees, is natural and is closely related, in the planar case, to some specializations of the cell-growth problem. Our goal is the enumeration, labelled and unlabelled, of k-gonal 2-trees according to the number n of k-gons. Wegive explicit formulas in the labelled case, and, in the unlabelled case, recursive and asymptotic formulas.
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Labelle, G., Lamathe, C., Leroux, P. (2002). Enumération des 2-arbres k-gonaux. In: Chauvin, B., Flajolet, P., Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science II. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8211-8_6
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DOI: https://doi.org/10.1007/978-3-0348-8211-8_6
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