On Fri, Mar 23, 2012 at 08:24:06AM -0400, msh...@math.vt.edu wrote: > It is easy to get the inversion set directly from any reduced word of the > Weyl group element. > > If w = s_{i_l} ... s_{i_2} s_{i_1} > > then the set of positive roots alpha such that w alpha is negative, is > > \alpha_{i_1}, s_{i_1} \alpha_{i_2}, s_{i_1} s_{i_2} \alpha_{i_3},... > > This produces "right inversions". If you want left inversions then > use w^{-1} (or use the reverse of the reduced word for w).
Good point. And if this is done right (by keeping track of the partial product s_{i_1}...s_{i_k}) this is roughly O(dr) where d is the rank of the root system and r is the length of the element. That is linear in the size of the output, which is as good as it can get. > If you are going to do this a lot then it can of course be done > recursively with remembering. Yup. Volunteer anyone? By the way: the reverse bijection could be useful too. Cheers, Nicolas -- Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> http://Nicolas.Thiery.name/ -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.