If you want the full character table then you can also do: sage: SymmetricGroup(Integer(5)).character_table() [ 1 -1 1 1 -1 -1 1] [ 4 -2 0 1 1 0 -1] [ 5 -1 1 -1 -1 1 0] [ 6 0 -2 0 0 0 1] [ 5 1 1 -1 1 -1 0] [ 4 2 0 1 -1 0 -1] [ 1 1 1 1 1 1 1]
>From memory this calls gap in the background, so using symmetric functions as Darij suggests will definitely be faster for individual entries and it may even be faster for the whole character table. Andrew On Friday, 20 December 2013 11:33:55 UTC+1, Amri wrote: > > Is there a fast implementation for characters values of symmetric groups > in Sage? It looks like > sage.combinat.symmetric_group_representations.pyconstructs the representation > explicitly to compute the character values. > In any case, it's not fast. > > I am looking for a function which, when fed two partitions ``la`` and > ``mu`` returns the value of the character of the Specht module > corresponding to ``la`` at a class with cycle type ``mu``. > > I would like something at least as fast as the Murnaghan-Nakayama formula > (Theorem 2.4.7 in *Representation Theory of the Symmetric Group* by James > and Kerber). I am also curious to know what the fastest known algorithm is. > > Thanks, > Amri. > -- 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.
