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Mar 20, 2019 at 18:42 comment added Sam Hopkins For anyone who sees this question later: it is worth contrasting the Dittmer-Pak paper with a paper of Cooper and Kirkpatrick (which extends the result of Wei mentioned by Richard Stanley above) which says that for "most" permutations $w$, the size of $[e,w]$ can be computed in sub-exponential time: arxiv.org/abs/1507.00388
Mar 13, 2019 at 17:07 comment added Sam Hopkins This is a terrific answer, thanks so much!
Mar 13, 2019 at 17:06 vote accept Sam Hopkins
Mar 13, 2019 at 17:02 history answered Hugh Denoncourt CC BY-SA 4.0