On 03/29/2007 11:38 PM, Nicolas M. Thiery wrote:
>> Hm, I don't think that's correct. It seems that the objects on the right are
>> linear orders, not permutations. (and that would indeed be in the book).
>
> Ach so! Sure, in that case I agree; with this point of view this the
> action is also by conjugation. Just make sure to point this out
> precisely in your documentation, as many users will have what you call
> linear orders in mind when they will see "permutation".
I've included the definition of the Permutation species including the
fact that the transport is via conjugation.
And I had from the beginning:
The \useterm{species of permutations} is closely related to the
\useterm{species of linear orders}. However, their isomorphism types
are different and, therefore, we cannot use \adtype{List} as the
representation but rather have to use the following in accordance with
the representation of \adtype{Partition}. For the generation of
isomorphism types we can easily borrow from the code for
\adtype{Partition}.
%
In fact, each list in the array presents a cycle in the cycle
decomposition of a given permutation.
%CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
<<representation: Permutation>>=
Rep == Array List L;
@
%TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
I hope you can relax now. :-)
Ralf
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