Hi Bruce, I'm working on King Tableaux along with my Professor. We came up with this algorithm to generate king tableaux from semistandard tableaux. If you could suggest a better algorithm, that would be great. Either way, I need help with writing the code. I'm new to Sage and Python as well. I hope that clears your confusion(apologies for that). Your help would be greatly appreciated.
Thanks, Soheli On Friday, March 6, 2020 at 3:06:35 AM UTC-5, Bruce wrote: > > 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/bbdc787b-a742-45e0-a6b6-359fcca0ad5f%40googlegroups.com.
