Superpermutations - Numberphile
392,716
Published 2018-01-29
This video features Dr James Grime.
More links & stuff in full description below ↓↓↓
More James Grime on Numberphile: bit.ly/grimevideos
James Grime: singingbanana.com/
Tackling the Minimal Superpermutation Problem: arxiv.org/abs/1408.5108
(Apparently I mucked up the copy/paste for the 1-6 superpermutation and, amazingly, people actually check this stuff... The full number is in the paper linked above)
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All Comments (21)
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Let's check...... YES, 1 contains all the permutations of 1.
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I love that moment at 3:38 "We don't know." "...no!"
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Dr Grime: "For 6 we don't know" Brady in total shock and awe: "No!?" Hilarious hahah gotta love the emotions one can get on these topics
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Whenever James checks the easy n=1 cases. I am always 1) slightly amused, and 2) very happy that he is so diligent about checking bases cases. There are a surprising number of wrong proofs that fail because the base case was not checked!
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"I counted the digits 10 times now, and it is still 1 digit short!" "This can't be true, count again, idiot!"
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Here is the scramble of James' Rubik's cube D B2 R2 F2 U R2 U' R2 U R2 B2 L' F D' F' B' R' D F2 L' U'
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"Superpermutations" sounds like a 90's math rock band
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suPERmutations
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6: Parker's superpermutation
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One less than expected after five steps? Sounds a lot like how the maximal number of divisions in a circle separated by n chords starts out as 2^n up to n = 5 but then falls away because it's actually the sum of five binomial coefficients. If, by some incredible miracle, this is analogous (and hey, binomial coefficients are factorial-related), we'd expect the solution for six to have length 2!+3!+4!+5!+6! = 872 and the solution for seven to have length 3!+4!+5!+6!+7! = 5910. That would be neat.
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I really like how much Dr. Grime seems to enjoy talking about numbers.
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I think the founder of Superpermutations missed the perfect idea to call them "SuPERmutations". Would have sounded much cooler.
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And I was thinking, "permutations aren't that interesting pretty much everything is known about it" My reaction when James said we don't know about 6 I was like no way. Numberphile never disappoints me
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Must do work, must not spend afternoon numbercrunching
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Is it just me, or is it far too long since we last saw James?
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It's so weird when you have a problem where you can evaluate the simplest cases almost by hand and you just add one or two and boom it becomes an unsolved problem.
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Why don't we call it supermutations? :'(
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I absolutely love those sequences that start to escalate very quickly and then there's some factor when James (or any host for that matter) turns to the camera and says "WE DON'T YET KNOW" cue the thriller music EDIT: and this time it's even better than some humongous undescribable number such as Graham's Number or TREE(3)! Amazing video and subject!
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I bet they counted to 872 alot of times.
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James Grime is one of my favourite hosts on this channel! Lovely video :)
