Hi Martin,
On 3/30/11 2:04 AM, Martin Rubey wrote:
Martin Rubey<martin.ru...@math.uni-hannover.de> writes:
"Nicolas M. Thiery"<nicolas.thi...@u-psud.fr> writes:
As for posets, I don't know. I would tend to first write a draft of
the method in Posets, and then decide if the interfaces and
implementations are similar enough to be shared or not.
Here goes:
# http://www.combinatorics.org/Volume_16/PDF/v16i2r9.pdf
...
def promotion(P, e):
...
I wonder about the following: maybe those classes that have a promotion
method could be "coercible" to a class LinearExtension depending on a
poset P, whose elements are linear extensions of P?
I.e., LinearExtension could have as input
* a standard Young Tableau
* a semistandard Young Tableau and an integer n
etc. (I know nothing about crystals...)
So I could write something like
sage: t = Tableau([[1,1,3],[2,3]])
sage: L = LinearExtension((t, 2))
sage: L.promotion()
[[1,1,2],[2,3]]
Would this make sense? (In particular, I'm not entirely sure whether
one would gain anything. I should stress that I'm *not at all* in
favour of replacing the existing methods ".promotion", the above is
intended as an additional feature.)
Usual semistandard tableaux are already defined on a totally ordered
alphabet {1,2,...,n+1}. So in this case, it would not add much.
However, if you want to define tableaux with entries in a poset, then
this could be useful. I suggest to leave this for another patch, however,
since it is orthogonal to the current patch.
Best,
Anne
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