Dear Soheli,
On Tue, Mar 03, 2020 at 03:12:09PM -0800, 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!
Disclaimer: I am not familiar with King tableaux.
Iterators are a comfortable tool in such situations. The general
structure for an iterator using a rejection method like yours would
be:
def kingTableaux(size,max_entry_val,to_generate):
for k in range(to_generate):
for t in SemistandardTableaux(size,max_entry=max_entry_val):
# Check all the conditions t should satisfy to be a king tableau
if / for ...:
# not a king tableaux; move on to the next onoe
continue
# Now we know t is a king tableau
yield t
This would be used as:
for t in kingTableaux(...):
...
If performance matters, and if King tableaux form a small subset of
semi standard tableaux, the next step would be to find a way to
produce them directly without generating all semistandard tableaux.
Possibly by induction. Or using a crystal structure on such tableaux
(relevant? https://arxiv.org/abs/1910.04459). Maybe someone already
has code for this.
Hope this help.
Cheers,
Nicolas
[1]
https://doc.sagemath.org/html/en/thematic_tutorials/tutorial-comprehensions.html#defining-new-iterators
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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