Séminaire Lotharingien de Combinatoire, B49z (2003), 34 pp.
Pierre Auger, Gilbert Labelle and Pierre Leroux
Computing The Molecular Expansion Of Species With The
Maple Package Devmol
Intuitively, the molecular expansion of a species F is a classification
of its structures according to their size and symmetries.
It can be seen as a refinement of the (ordinary) generating function
for the number of unlabelled F-structures of size n.
The goal of the Maple package Devmol is to compute such molecular
expansions, up to a specified degree, for species of the so-called
cyclo-set type (in French: espèces cyclo-ensemblistes).
These are species which have either an explicit or a recursive definition
in terms of the species L, of lists, E, of sets, and C,
of oriented cycles.
In this paper, we first recall some basic results about molecular
expansions. In particular, we give some examples of molecular expansions,
namely for the species of "Rooted trees" and of "Husimi graphs",
weighted by their block-size distribution. We also describe briefly the
addition formulas for the basic species which are essential for the
recursive computation of molecular expansions.
Subsequently, we give a detailed description of the package
Devmol, and we conclude with two examples of applications,
to rooted trees weighted by a leaf counter and to connected graphs,
all of whose blocks are in a given family B of species of cyclo-set
Received: April 16, 2003.
Revised: July 18, 2003.
Accepted: October 15, 2003.
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