A classification of plane and planar 2-trees

摘要

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, Graphical Enumeration, Academic Press, New York, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e. a classification of their structures according to their stabilizers. Therein result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is related to the enumeration of polyene hydrocarbons of molecular formula CnHn+2. (C) 2003 Elsevier B.V. All rights reserved. [References: 17]