On 3/30/11 6:06 AM, Martin Rubey wrote:
Anne Schilling<a...@math.ucdavis.edu> writes:
sage: t = Tableau([[1,1,3],[2,3]])
sage: L = LinearExtension((t, 2))
sage: L.promotion()
[[1,1,2],[2,3]]
Usual semistandard tableaux are already defined on a totally ordered
alphabet {1,2,...,n+1}. So in this case, it would not add much.
Yes, it only gives a different view on the tableau. (I hope there is no
misunderstanding: the poset structure comes from the shape of the
tableau, the linear extension from the entries. The example was in fact
stupid: for semistandard tableaux we don't really have a linear
extension.)
You want to view standard tableaux as paths in the partition lattice, right?
For semistandard tableaux one needs to choose an order for repeated letters.
This is what you had in mind for your linear extension, right? In the current
patch the order chosen is from left to right (which agrees with the usual
standardization process of semistandard tableaux).
However, if you want to define tableaux with entries in a poset, then
this could be useful.
Hm, I never came across a tableau with entries in a non-totally-ordered
set, so far. Did you?
I suggest to leave this for another patch, however, since it is
orthogonal to the current patch.
Of course, it has nothing to do with the current patch. The only
question is whether it might be useful at all.
Feel free to add this to sage if it is useful to you!
Best,
Anne
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