Hi Martin, hi Ralf,
> Nicolas, how do you produce the elements of unlabelled combinatorial
> classes? But somehow I guess that for Plus and Times (I.e., Union
> and Cross) it should be possible / easy. Unfortunately, I don't
> have mupad currently...
Plus and Times are indeed done straightforwardly as in the labelled
case (it's even a little bit easier, as you don't have to manipulate
the labels). On the other hand, as soon as there is a non trivial
group G acting, things start to be more difficult. We don't do the
general case: as you mentioned, it includes for example the generation
of unlabelled graphs, which is *hard*.
For the Sets, Multisets, Cycles, Lyndon constructors, there are fast
(Constant Amortized Time) special-purpose generation algorithms. For
example the generation of Cycles and Lyndon use Joe Sawada's
algorithms which dates back from just 2003. There are also algorithms
for ranking/unranking Sets and Multisets. But just to had a little bit
of salt in the discussion: it is currently *not known* if it is
possible to efficiently unrank Cycles.
Cf. X. Molinero's thesis for an overview.
Cheers,
Nicolas
PS: Although I am quite silent, I am following what you both are
doing. This sounds really promising!
--
Nicolas M. Thiéry "Isil" <[EMAIL PROTECTED]>
http://Nicolas.Thiery.name/
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