#18014: is_ribbon on skew tableaux and skew partitions don't really check for
ribbonness
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: ribbon, partition, skew | Merged in:
partition, tableau, sage-combinat, days64 | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Description changed by darij:
Old description:
> Being a ribbon means not just containing no 2x2 squares; it also means
> being connected.
>
> {{{
> sage: SkewPartition([[3,1],[2]])
> [3, 1] / [2]
> sage: _.is_ribbon()
> True
> }}}
>
> Good news is that these methods seem to never be used.
New description:
Being a ribbon means not just containing no 2x2 squares; it also means
being connected.
{{{
sage: SkewPartition([[3,1],[2]])
[3, 1] / [2]
sage: _.is_ribbon()
True
}}}
Good news is that these methods seem to never be used.
A correct way to check if a skew partition `\lambda / \mu` is a ribbon is
the following: Let `u` be the smallest positive integer for which
`\lambda_u > \mu_u`. Let `v` be the largest integer greater (strictly
greater!!) than `u` for which `\lambda_v = \mu_{v-1} + 1`. If every `i >
v` satisfies `\lambda_i = \mu_i`, then `\lambda / \mu` is a ribbon;
otherwise it is not.
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Ticket URL: <http://trac.sagemath.org/ticket/18014#comment:2>
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