#18686: Tableaux: remove false theorem I stated about Bender-Knuth involutions
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: combinatorics | Keywords: tableaux, bender-
Merged in: | knuth involutions, sage-combinat,
Reviewers: | beginner
Work issues: | Authors: Darij Grinberg
Commit: | Report Upstream: N/A
33c3a7bb5243ba4244451255fb2bb007f12ed8a5| Branch:
Stopgaps: | u/darij/benderknuth
| Dependencies:
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I claimed that `(s_i s_{i+1})^6 = id`, where `s_k` means the `k`-th
Bender-Knuth involution on semistandard skew tableaux. I even made a
doctest that unfortunately used a hook shape, which renders the Bender-
Knuth involutions rather boring (though maybe it would make a nice
exercise to check it in this case -- although I don't know if it is always
true there).
The claim is false. There is a counterexample for skew tableaux and `i =
1` (or straight tableaux and `i = 2`). The source where I had it from, a
paper by Berenstein and Kirillov, only claimed it for straight tableaux
and `i = 1` (and that is indeed correct).
Thanks to Pavel Galashin for finding a counterexample!
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Ticket URL: <http://trac.sagemath.org/ticket/18686>
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