Dear all,
I made some progress concerning the isomorphism types of compose. However, as I
reported previously, my current approach requires to generalize
isomorphismTypes to take a multiset as input. Furthermore,
isomorphismTypes$SetPartition now generates multisets of multisets.
For example,
[isomorphismTypes({{1^3}})$SetPartition]
returns
[{{1^3}},{{1^2},{1}},{{1}^3}]
i.e., integer partitions of 3, while
[isomorphismTypes({{1^2},{2}}])$SetPartition]
returns
[[{{1^2,2}},{{1^2},{2}},{{1,2},{1}},{{1}^2,{2}}]
Finally
[isomorphismTypes({1,2,3}])$SetPartition]
returns the usual set partitions.
But then, what is the signature of isomorphismTypes$CombinatorialSpecies ? I
definitively need help here!
It is tempting to make the Representations in the species more general to
accomodate both structures and isomorphismtypes. I guess, this will work well,
as long as there are no operations with signature "% -> something" in
CombinatorialSpecies, but this will probably be the case at some point.
Martin
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