Dear Ralf, Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> Dear Ralf, Hi Ralf! > On 03/11/2007 03:25 PM, Ralf Hemmecke wrote: > > Could someone tell me what the cycle type of \sigma \in S_0 is. > > I somehow think that (), i.e. the empty tuple is a good candidate. > > What else. Hmmm, I wanted to say the sequence which consists of zeros only. Well, that's about the same thing, I guess :-) > > Take n=0 in Definition 2.2.4 of BLL. What happens? Let \sigma\in S_0. So, \sigma is the only permutation of the empty set. Something rather imaginary... There is exactly one such permutation, which explains 0!=1. Note that - since it is a function from the empty set to the empty set, one cannot really say that it takes an argument :-) > > What is G[\sigma]? Ah, sure, it is a permutation in some S_m. First > > question: what is m? > > The only good choice is m=\card G[0]. And to be functorial G[\sigma] must be > the identity permuation of S_m. I just wanted to look that up. OK, I did: one can say (although I don't really have a good argument for that) that the sigma above is the identity on the empty set... Note that axiom says lcm(0,n)=0 for any n. > So I would be happy if someone could confirm my thinking. confirmed? 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
