I think I fixed your formatting… not sure why it was giving you trouble before! That is super interesting, I wasn’t aware of these generalized “cyclic Knuth” moves, thanks for sharing!

Maria

]]>although i prefer brackets since you don’t need to use the shift key or reach as far, plus it won’t be confused with a government agency: BEMA or [EMA]

]]>It turns out that the set of cyclic orders of [n] becomes a graded poset of length $\binom{n}{3}$ under this operation, with unique minimal element $n(n-1) \cdots 21$ and unique maximal element $12\cdots (n-1)n$. See https://arxiv.org/abs/0909.5324 for a more general statement related to an arbitrary affine Coxeter group, and see 2010 USAMO Problem 2 for a fun restatement.

Let me know if this seems inteeresting/useful to you!

]]>Anyway, let me know if it seems interesting!

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