Oh, I forgot something:
about that ranking and unranking business.
Wouldn't it be a possibility to introduce a new type LinearSpecies, where
constructors take an ordered list of elements?
There is a natural way to go from CombinatorialSpecies to LinearSpecies, (BLL
Section 5.1, Remarque 5) but I'm not sure what one actually gets.
Can one make both the "labelled" and the "unlabelled" things into Linear
Species? There is a hint in BLL, just befor Definition 7, Section 5.1: (I try
to translate to English)
One has to choose between ordinary generating series (as in Joyal[140],
Section 4) or exponential generating series (as in Foata[93]).
-------------------------------------------------------------------------------
Ralf, I just had the idea of introducing a CombinatorialSpecies Matroid as an
example. Although, I guess, it will be quite hard to implement, it will
certainly be interesting and serve as a nice illustration of the ideas in
aldor-combinat.
structures([1,2,3,4])$Matroid(Integer) should return a set of all matroids on
four
elements, with arbitrary rank.
(A matroid is a "ground set", above: {1,2,3,4}, together with a set of "bases",
each a subset of the ground set, all of the same cardinality, so that they
satisfy the exchange condition:
for any two bases B1, B2 and x in B_1\B_2
there is a y in B_2\B_1,
such that (B_1 u y)\{x}
Martin
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