While looking into the code on skew Schur functions, I noticed this:
elif x in sage.combinat.skew_partition.SkewPartitions():
import sage.libs.lrcalc.lrcalc as lrcalc
skewschur = lrcalc.skew(x[0], x[1])
return self._from_dict(skewschur)
This has the following result:
sage: s = SymmetricFunctions(QQ).s()
sage: e = SymmetricFunctions(QQ).e()
sage: sp = SkewPartition([[5,3,3,1], [3,2,1]])
sage: e(s(sp))
e[2, 1, 1, 1, 1] - e[2, 2, 1, 1] - e[3, 1, 1, 1] + e[3, 2, 1]
sage: e(sp)
e[2, 2, 1, 1] + e[2, 2, 2] + e[3, 1, 1, 1] + 3*e[3, 2, 1] + e[3, 3] + 2*e[4,
1, 1] + 2*e[4, 2] + e[5, 1]
The skew() function of lrcalc returns the corresponding skew Schur
function, so the above is a bug. My question is should we
(A) raise an error for skew shapes on all bases,
(B) allow only of the Schur basis, or
(C) construct the skew Schur function and convert to the corresponding
basis.
I'm not so sure about (C) because this would mean skew partitions behave
very differently than for partitions. I'm leaning towards (B). Thoughts?
I'm also going to add a method skew_schur() which constructs the skew Schur
function, as to make getting at skew Schur functions easier (there is also
right now the skew_by method, but that acts on elements).
Best,
Travis
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