Ralf Hemmecke <[EMAIL PROTECTED]> writes:

> > In any case, this should be convincing evidence to write p_i instead of x_i
> > and interpret the cycle index series as a symmetric function.
> 
> You are probably not saying that instead of x you want to use the letter p
> instead. That would be ridiculous.

Well, perhaps it sounds ridiculous, but I am saying exactly that.  And,
additionally, we should keep in mind that we really are working with symmetric
functions.

> As you have shown, one only has to take the CIS, substitute for the x_i some
> symmetric polynomials and voila, you get what you want. Why is that so
> problematic?

It isn't.  Only, good notation is often very useful.  You see, substituting for
the x_i other symmetric functions (not polynomials, by the way), we do not get
anything sensible.

> As I understand BLL, we should rather consider (extend AC to) weighted
> species. That is how you get your substitutions. Am I wrong?

No, I don't think so, but to be honest, I don't know.  In any case, we cannot
start yet another project.  multisort is difficult enough, and in any case far
more important than weights.

Martin


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