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


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