"Nicolas M. Thiery" <[EMAIL PROTECTED]> writes: > > Are you sure? > > This was explained to me by François Bergeron, so pretty much yes :-) (up to > the point that we are speaking about the same thing). Actually, I think he > told me this example was in the Book. > > The point is that relabeling a permutation in cycle notation corresponds to > the action of S_n on itself by *conjugation*, and not *on the right* as when > you relabel a permutation in array notation. > > Example, relabeling by the transposition (1,2): > > (1,2) (3) = 213 > > || || > \/ \/ > > (1,2) (3) <> 123
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). By the way, using species, you cannot represent a permutation as 213, since you don't have an ordering on the input set. Thus, you really have 123 213 For clarity, let's rather write abc bac Now, how is the relabeling going to work, if you relabel a->1, b->2, c->3 ? It must be 123 213 By analogy, relabeling 1->2, 2->1, 3->3, you obtain 213 123 which does agree with (1 2) (3). Martin ------------------------------------------------------------------------- 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
