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From: GeometricGroup on 21 May 2010 01:26 > On 20 May, 14:54, GeometricGroup <ggx...(a)gmail.com> > wrote: > > The detailed Coxeter graph of my question is found > in > > > > > http://www.combinatorics.org/Volume_5/PDF/v5i1r18.pdf > > > > (In page 5, the first figure in table 1) > > > > I just started learning this stuff, so it confuses > me a lot. > > > > Thanks for any help. > > You have removed the context! > > Properties 1 and 2 that you mentioned in your earlier > post > (corrected): > > > Let \tilde{S_n} be affine symmetric group. Elements > x \in \tilde{S_n} are bijections from Z to itself > satisfying: > > > > 1. x(i+n)=x(i)+n for all i \in Z. > > 2. \sum_{i=1}^n x(i)=(n+1)C2, where nCr denotes "n > choose r". > > are Lemma 4 and Proposition 9 of the paper you cited > above. > > Derek Holt. > I was wondering where n+1C2 come from, but it turns out that it is simply the sum from 1 to n. Thank you for your help. |