On Sat, Mar 6, 2010 at 9:26 PM, bump <b...@match.stanford.edu> wrote:
> > On Mar 6, 3:52 pm, Pedro Sanchez <pdsanc...@gmail.com> wrote: > > > > consider also the code in > There should actually be two versions of this. This version (as Anne > said) > relates nxn matrices with nonnegative integer values to pairs of > tableaux with > the same shape. There should also be a bijection between nxn matrices > with > values 0 and 1 to pairs of tableaux with conjugate shapes. > > Yes, the so called dual RSK, although it's trickier to implement Since row_insertion, bump, schensted insert and friends return the new table, the "as is" version of RSK says "insert bottonw row of the array to get P, take Q as the register table filled with the upper row" The symmetry theorem however allows you to construct Q using insertion: if you start with the matrix A, you transpose it, new two-row array will have rows switched and reordered (so it's still lexicographically ordered). However, on 0-1 matrices you use column bump with bottom row for P and conjugate sliding for Q with top row. And then things get hairy (snce you need to track which square was added to P on each step in order to slide it). Symmetry theorem won't help as is, since starting with A^t won't give you (Q,P) but some other pair related to dual Burge's correspondence. Q tableau can however be described using insertions (after all Burge's correspondence is also insertion) but you need to do some shuffling around. > > it's been a great down for me that only the case "permutation (matrices) > > <--> permutations <--> standard tableau" is handled by sage > > > > But my coding skills aren't up to the task of implementing it and > submitting > > it > > This sounds like a good way to acquire some coding skills! If there's > implementation > or programming issues I think it would be appropriate to discuss them > here, if you want to > try it. > > Dan > > > Actually I have coded such insertions for my own study, it's the "integrating to sage" part which frightens me a bit (I never understood how to "redefine" a bultin function to make a trivial change , see http://trac.sagemath.org/sage_trac/ticket/8322 so I just passed it along ;) > -- > 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-de...@googlegroups.com. > To unsubscribe from this group, send email to > sage-combinat-devel+unsubscr...@googlegroups.com<sage-combinat-devel%2bunsubscr...@googlegroups.com> > . > 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-combinat-devel" group. To post to this group, send email to sage-combinat-de...@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.
