Hi again!
Is the promotion operator on arbitrary tableaux already in sage?
I think I once implemented the promotion operator on rectangular tableaux as
sage: t = Tableau([[1,2],[2,3]])
sage: t.promotion(2)
[[1, 2], [3, 3]]
sage: t
[[1, 2], [2, 3]]
There is also a strange promotion_operator which seems to add boxes to a
tableau,
but there is no explanation what it does. Perhaps it is a misnomer?
def promotion_operator(self, i):
EXAMPLES::
sage: t = Tableau([[1,2],[3]])
sage: t.promotion_operator(1)
[[[1, 2], [3], [4]], [[1, 2], [3, 4]], [[1, 2, 4], [3]]]
sage: t.promotion_operator(2)
[[[1, 1], [2, 3], [4]],
[[1, 1, 2], [3], [4]],
[[1, 1, 4], [2, 3]],
[[1, 1, 2, 4], [3]]]
sage: Tableau([[1]]).promotion_operator(2)
[[[1, 1], [2]], [[1, 1, 2]]]
sage: Tableau([[1,1],[2]]).promotion_operator(3)
[[[1, 1, 1], [2, 2], [3]],
[[1, 1, 1, 2], [2], [3]],
[[1, 1, 1, 3], [2, 2]],
[[1, 1, 1, 2, 3], [2]]]
TESTS::
sage: Tableau([]).promotion_operator(2)
[[[1, 1]]]
sage: Tableau([]).promotion_operator(1)
[[[1]]]
Best,
Anne
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