Hi, Oops, per popular request, let me be a bit more specific:
> what is "CAT complexity" Constant Amortized Time; roughly speaking this means that, in average, each step of the iteration takes a constant amount of time: http://stackoverflow.com/questions/200384/constant-amortized-time In practice, since we usually create a full new element at each step of the iteration, we can't really achieve CAT; so it's fair to aim at an amortized time complexity that is linear in the size of the elements that are iterated through. > and how can one use crystal operations for generation of all SSYT? > Do they form a connected digraph on the set of all SSYT with given > max_entry and shape?) Precisely. You get all SSYT from the highest weight one by applying successively the f (or e? I never know) crystal operators: sage: CrystalOfTableaux(['A',2], shape = [3,2]).list() [[[1, 1, 1], [2, 2]], [[1, 1, 2], [2, 2]], [[1, 1, 3], [2, 2]], [[1, 1, 3], [2, 3]], [[1, 2, 3], [2, 3]], [[1, 1, 3], [3, 3]], [[1, 2, 3], [3, 3]], [[2, 2, 3], [3, 3]], [[1, 1, 1], [2, 3]], [[1, 1, 2], [2, 3]], [[1, 2, 2], [2, 3]], [[1, 1, 1], [3, 3]], [[1, 1, 2], [3, 3]], [[1, 2, 2], [3, 3]], [[2, 2, 2], [3, 3]]] And there is a way to build an iterator out of those operations that is essentially CAT; see ClassicalCrystals.ParentMethods.__iter__. 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 unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
