On 02/16/2007 10:25 AM, Nicolas M. Thiery wrote:
>> If (f pleth g) is defined as sum_{k=0}^\infty g_k*f(z^k) I also get 1
>> since the only non-zero term is for k=0.
> For k=0, you get g_0 ( f_1 z^(1*0) + f_2 z^(2*0) + ...) = \infty as well.
Thanks for repeating again and again, but only now I see that for two
power series f(x) and g(x) in general
f(g(x)) \neq (f pleth g)(x).
>> If plethysm corresponds to substitution then there is something I don't
>> understand.
>
> To substitution of *combinatorial classes*. Not of power series.
Yes, now I see that the operation is different. I was probably misled by
the fact that the (exponential) generating series of the composition (or
substitution) of two species F and G is given by F(G(x)). (BLL, Thm. 1.4.2)
>> Where does the plethysm of _univariate_ series come into play in
>> Mupad-Combinat?
> It's the basic tool to get the generating series for unlabelled Set(A)
> / multiset(A) / Cycle(A) / Lyndon(A) knowing the generating series for
> A. See those functions in countingFunctions. It's should be used at
> some point in combinat::decomposableObjects.
Oho. I haven't thought about it, since in the same theorem the
isomorphismtype series
(F \circ G)^\tilde (x) = Z_F(g(x), g(x^2), g(x^3), ...)
with g = \tilde(G).
What you are saying is that (F \circ G)^\tilde can be computed without
knowing the cycle index series???
> Sure, we put on the web the documentation of the stable version. The
> latest version is fetchable from our CVS.
Do you also have an SVN repository? On SF I could not find a reference.
Ralf
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