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18686 Tableaux: remove false theorem I stated about Bender-Knuth involutions darij "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!" defect closed major sage-6.8 combinatorics fixed tableaux, bender-knuth involutions, sage-combinat tscrim aschilling sage-combinat nthiery jkeitel jpswanson MariaMonks Darij Grinberg Travis Scrimshaw N/A 7deac5cff145d9b4f79428331129727591a461ab 7deac5cff145d9b4f79428331129727591a461ab