Dear Nicolas, Thank you for helping me. I created the function:
sage: def is_king_tableau(t,no_of_rows): ....: for i in range(no_of_rows): ....: if t[0][0] != 1: ....: return False ....: elif t[i][0] <= 2*i: ....: return False ....: else: ....: i=i+1 ....: return True ....: sage: t=SemistandardTableau([[1,1,2],[3,4],[5,8],[6,9]]);t [[1, 1, 2], [3, 4], [5, 8], [6, 9]] sage: is_king_tableau(t,4) False sage: t=SemistandardTableau([[1,1,2],[3,4],[5,8],[7,9]]);t [[1, 1, 2], [3, 4], [5, 8], [7, 9]] sage: is_king_tableau(t,4) True What do you think? Were you suggesting something like this? Thanks, Soheli On Friday, March 6, 2020 at 1:16:57 PM UTC-5, Nicolas M. Thiery wrote: > > Dear Soheli, > > Thanks for the extra info. As a first step I suggest that you write a > little function that takes a semi standard tableau and test whether > it's a king tableau. > > def is_king_tableau(t): > ... > > Cheers, > Nicolas > > On Fri, Mar 06, 2020 at 08:29:33AM -0800, Soheli Das wrote: > > 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 <javascript:>. > > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-combinat-devel/bbdc787b-a742-45e0-a6b6-359fcca0ad5f%40googlegroups.com. > > > > Nicolas > -- > Nicolas M. Thiéry "Isil" <nth...@users.sf.net <javascript:>> > 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-combinat-devel/ca7fbb7b-41ef-4f7b-bfe8-9d4c90bb25e1%40googlegroups.com.
