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.)

Martin

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