A classification of plane and planar 2-trees

Details A classification of plane and planar 2-trees A classification of plane and planar 2-trees

2002-02-06

arxiv.org/abs/math/0202052v1

Theorical Computer Science, 307 (2003), 337-363

Mathematics

Combinatorics

26 pages, 14 figures

Scientific paper

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 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. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.

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