On Tue, Apr 24, 2012 at 3:46 AM, Nathann Cohen <[email protected]> wrote: > Helloooooo everyody !!! > > I am writing a patch for the recognition of Permutation graphs (and > comparability graphs, actually), and I thought that it would be nice > to have some way to plot the permutations built this way. Given a > permutation p on 1...n, you get the permutation graph by linking > together two vertices ij such that i<j and p(i) > p(j). Hence the kind > of plot I have in mind is the one you can see on the top-right corner > of his page : > > http://en.wikipedia.org/wiki/Permutation_graph > > I intended to write it, but there are two questions that need an > answer before doing that > > 1) Is it aready implemented in Sage somewhere ? I did not see it, but well :-) > 2) Is it useful to add it as a method of Permutation ? That is, should
I vote yes. When I teach this, I call this the swapping diagram (not standard terminology). The number of swaps gives you the Bruhat length, if I remember correctly, when you regard S_n as a Coxeter group. The parity gives you the sign of the permutation, which gives you, in turn, the determinant of the associated matrix. It is a very useful diagram:-) > it be implemented there or rather as a part of my recognition > algorithm, if it is only of interest for graph theoreticians ? > > Thaaaaaaaaaaaaaaaaanks ! :-) > > Nathann > > -- > You received this message because you are subscribed to the Google Groups > "sage-combinat-devel" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sage-combinat-devel?hl=en. > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
