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The Specification of 2-trees

✍ Scribed by Tom Fowler; Ira Gessel; Gilbert Labelle; Pierre Leroux

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
187 KB
Volume
28
Category
Article
ISSN
0196-8858

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✦ Synopsis

We derive new functional equations at a species level for certain classes of 2-trees, including a dissymmetry theorem. From these equations we deduce various series expansions for these structures. We obtain formulas for unlabeled 2-trees which are more explicit than previously known results. Moreover, the asymptotic behavior of unlabeled 2-trees is established.  2002 Elsevier Science (USA) Nous présentons de nouvelles équations fonctionnelles pour certaines classes de 2-arbres, incluant un théorème de dissymétrie. Nous en déduisons diverses séries génératrices associées à ces espèces. Nous obtenons ainsi des formules énumératives pour les 2-arbres non-étiquetés qui sont plus explicites que les résultats connus jusquà présent. De plus le comportement asymptotique de ces structures est établi.

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## Abstract A graph __G__ is a 2‐tree if __G__ = __K__~3~, or __G__ has a vertex __v__ of degree 2, whose neighbors are adjacent, and __G__/ __v__ is a 2‐ tree. A characterization of the degree sequences of 2‐trees is given. This characterization yields a linear‐time algorithm for recognizing and r