Labelled and unlabelled enumeration of k-gonal 2-trees

P. Auger, G. Labelle, P. Leroux, Computing the molecular expansion of species with the Maple package Devmol, Séminaire Lotharingien de Combinatoire, Article B49z, 2003, 34p. (http://euler.univ-lyon1.fr/home/slc) Beineke, 1969, Several proofs of the number of labeled 2-dimensional trees, 11 Bender, 1974, Asymptotic methods in enumeration, SIAM Rev., 16, 485, 10.1137/1016082 Bergeron, 1998, Combinatorial Species and Tree-like Structures, Vol. 67 Bona, 1996, Enumeration of m-ary cacti, Discrete Math., 157, 227 T. Fowler, I. Gessel, G. Labelle, P. Leroux, Specifying 2-trees, in: D. Krob, A.A. Mikhalev, A.V. Mikhalev (Eds.), Proceedings FPSAC’00, Moscow, June 26–30, 2000, Springer, Berlin, pp. 202–213. Fowler, 2002, The specification of 2-trees, Adv. Appl. Math., 28, 145, 10.1006/aama.2001.0771 Harary, 1973 Harary, 1975, On the cell-growth problem for arbitrary polygons, Discrete Math., 11, 371, 10.1016/0012-365X(75)90041-2 INRIA, Encyclopedia of combinatorial structures, http://algo.inria.fr/encyclopedia/index.html. Joyal, 1981, Une théorie combinatoire des séries formelles, Adv. Math., 42, 1, 10.1016/0001-8708(81)90052-9 T. Kloks, Enumeration of biconnected partial 2-trees, 26th Dutch Mathematical Conference, 1990. T. Kloks, Treewidth, Ph.D. Thesis, Royal University of Utrecht, Holland, 1993. G. Labelle, Some new computational methods in the theory of species, Combinatoire énumérative, Proceedings, Montréal, Québec, Lectures Notes in Mathematics, Vol. 1234, Springer, New York, Berlin, 1985, pp. 160–176. G. Labelle, C. Lamathe, P. Leroux, Développement moléculaire de l'espèce des 2-arbres planaires, Proceedings GASCom’01, 2001, pp. 41–43. G. Labelle, C. Lamathe, P. Leroux, Enumération des 2-arbres k-gonaux, in: B. Chauvin, P. Flajolet, et al. (Eds.), Second Colloquium on Mathematics and Computer Science, Versailles, September 16–19, 2002, Trends in Mathematics, Birkhauser, Basel, Switzerland, 2002, pp. 95–109. Labelle, 2003, A classification of plane and planar 2-trees, Theoret. Comput. Sci., 307, 337, 10.1016/S0304-3975(03)00224-X G. Labelle, C. Lamathe, P. Leroux, Dénombrement des 2-arbres k-gonaux selon leur taille et leur périmètre, Ann. Sci. Math. Québec, 2003, submitted. Labelle, 1996, Enumeration of (uni-or bi-colored) plane trees according to their degree distribution, Discrete Math., 157, 227, 10.1016/S0012-365X(96)83017-2 Otter, 1948, The number of trees, Ann. Math., 49, 583, 10.2307/1969046 Palmer, 1969, On the number of labeled 2-trees, J. Combin. Theory, 6, 206, 10.1016/S0021-9800(69)80121-3 Palmer, 1973, On the number of plane 2-trees, J. London Math. Soc., 6, 583, 10.1112/jlms/s2-6.4.583 Prüfer, 1918, Neuer Beweis eines Satzes über Permutationen, Arch. Math. Phys., 27, 742 N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/~njas/sequences. Sloane, 1995