>> p_n[g] = g[p_n] >> Seemingly, plethysm is commutative by definition, but my eyes don't see a >> definition of a plethysm of two arbitrary elements of K[[p]]. > > No, if I'm not completely mistaken, the plethysm is not commutative. Only for > power sums.
Oh, shame on me. I gave a polynomial example of non-commutativity myself in http://article.gmane.org/gmane.comp.mathematics.aldor-combinat.devel/605 f=x+x^2, g=x^2 f(g) = x^2 + (x^2)^2 g(f) = (x+x^2)^2 Just read x=p_1. >> I can only see a definition f[g] where at least one (either f or g) is a >> polynomial. Don't you agree? > No. Expand f and g in terms of the power sum symmetric functions and apply the > definitions above. Sorry, but I don't agree. And you probably see it if you Assume that we would not have K[[p]] but K[p]. The definition only says something about *finite* sums. I cannot see something that allows me for f = \sum_{t\in T} c_t t (where T is the (commutative) monoid of powerproducts in x_1,x_2,x_3,...) and another g \in K[[p]] to say f[g] = \sum_{t\in T} c_t t[g]. This "extended by" of Mishna p.29 I usually read as a *finite* iteration. Ralf ------------------------------------------------------------------------- Take Surveys. Earn Cash. Influence the Future of IT Join SourceForge.net's Techsay panel and you'll get the chance to share your opinions on IT & business topics through brief surveys-and earn cash http://www.techsay.com/default.php?page=join.php&p=sourceforge&CID=DEVDEV _______________________________________________ Aldor-combinat-devel mailing list Aldor-combinat-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/aldor-combinat-devel
