#19218: Restrict skew partition input to Schur basis and implement a skew Schur
method
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Reporter: tscrim | Owner: sage-combinat
Type: defect | Status: new
Priority: major | Milestone: sage-6.9
Component: | Keywords: schur, symmetric functions
combinatorics | Authors: Travis Scrimshaw
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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If you pass a skew partition to a basis of the symmetric functions, you
get what should be the skew Schur function:
{{{
sage: sp = SkewPartition([[5,3,3,1], [3,2,1]])
sage: e = SymmetricFunctions(QQ).e()
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]
}}}
This would be corresponding skew Schur function if it was in the Schur
basis, however we have
{{{
sage: s = SymmetricFunctions(QQ).s()
sage: e(s(sp))
e[2, 1, 1, 1, 1] - e[2, 2, 1, 1] - e[3, 1, 1, 1] + e[3, 2, 1]
}}}
This ticket will make skew partition input only valid for Schur functions
and implement a method `skew_schur` which handles creating skew Schur
functions.
--
Ticket URL: <http://trac.sagemath.org/ticket/19218>
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