Dear Soheli, Your post does not have a question so I am not sure if you are asking for help on getting started with writing code or whether you are asking for a better algorithm.
I am really following up on Nicolas' post and discussing the algorithm. The history is that crystal operators on King tableaux are not obvious (and maybe not known), De Concini came up with a different definition which does accomodate crystal operators. A bijection between these two tableaux was given by Sheats. I believe (but don't have details) that the motivation for Ron King was that his definition corresponds to symmetric (or antisymmetric) Gelfand-Tsetlin patterns. This suggests that you could approach this by constructing an iterator for (anti?)-symmetric Gelfand-Tsetlin patterns. Best, Bruce On Tuesday, 3 March 2020 23:13:51 UTC, Soheli Das wrote: > > I'm trying to generate a function that produces King tableaux. My idea is > to first generate Semi-standard tableaux and then select the ones that obey > the conditions of a King tableaux. I'm thinking of the entries i and -i for > i=1,....,n as entries 1,....,2n. So, basically I want the rows to be weakly > increasing and the columns to be strictly increasing like 1<3<5<.....<2n-1. > The following is what I have so far, it simply generates semistandard > tableaux. > > def generate_kingTableaux(size,max_entry_val,to_generate): > ....: v=[ ] > ....: for k in range(to_generate): > ....: > v.append(SemistandardTableaux(size,max_entry=max_entry_val).list()) > ....: return v > > I want to implement a condition which is somewhat like: if v[i][1] < 2i-1 > then not a king tableaux; else i=i+1. > I'm not sure how to implement this in sage. I would really appreciate if > someone could guide/help me! > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-combinat-devel/634a89f6-4fb9-4010-89b5-3ad784d81b8f%40googlegroups.com.
