#17252: bug fix in StrongTableaux.marked_CST_to_transposition_sequence
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Reporter: zabrocki | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.4
Component: combinatorics | Keywords:
Merged in: | Authors: Mike Zabrocki
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Anne Schilling pointed out the following error in the algorithm to convert
a strong marked column strict tableau to a sequence of transpositions:
{{{
sage:
StrongTableaux.marked_CST_to_transposition_sequence([[-1,-2,-2,-2,-2],[-2,2],[2]],3)
[[4, 5], [3, 4], [2, 4], [2, 3], [1, 2], [0, 1]]
}}}
however the answer should be `[[4,5],[3,4],[2,3],[1,2],[-1,0],[0,1]]` and
the problem arises because it was never clear in the algorithm for
converting a marked column strict tableau into a sequence of
transpositions what conditions I need to check to make sure I was applying
a valid transposition. In fact, there was a comment in the code that
indicated my worry that one might be able to apply two transpositions and
reduce the length by 1.
This is exactly what happens in this case because if you apply the
sequence of transpositions t_{2,4} on t_{3,4} t_{4,5} T then in fact
t_{2,4} does reduce the length of shape of the tableau by 1, but there are
no cells of content 2 and 3 in the tableau t_{3,4} t_{4,5} T.
It looks like there are a couple of ways of catching this condition. It
might be sufficient to check that applying the transposition t_{2,4} is
not valid (because it really should be applying t_{-2,0} instead). That
fix might or might not be sufficient (and a counterexample will be
difficult to identify). To be more thorough, I will verify that if t_{ij}
decreases the length of the core by 1, then the labels of the cells in
range(i,j) that are removed include exactly one negative label.
--
Ticket URL: <http://trac.sagemath.org/ticket/17252>
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