> Another question: I would like to search for a statistic (on permutations,
> but the question applies in general) that satisfies addtitional structural
> constraints (eg., it should be invariant under conjugation with the long
> cycle).  Is such a search also possible?

The obvious solution is to take the FindStat output and check if the
given outputted statistic satisfies your constraints. I currently
cannot think of any more sophisticated things to do there, but maybe
you have something in mind...

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