Timeline for What is the fairest order for stage-striking (and is it the Thue-Morse sequence)?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2018 at 6:28 | comment | added | Harry Altman | So this is interesting -- it seems like Thue-Morse doesn't consistently do better than alternating (or "snaking", i.e. repeating $0110$ over and over), but reverse Thue-Morse looks like it consistently does better than all of these, even though it's not the minimum. | |
| Nov 28, 2018 at 5:27 | comment | added | Harry Altman | Huh, so it's not unique. I wasn't expecting an answer there so fast! But now with Raphael's recursion it's easy. I'll have to go write a thing to compute that so I can try some other things with this. Thanks again! | |
| Nov 27, 2018 at 23:26 | comment | added | Claude Chaunier | The fairest difference for $n=16$ is $0$ as it is for $n=6$. What is the next such $n$ ? | |
| Nov 27, 2018 at 22:17 | history | edited | Claude Chaunier | CC BY-SA 4.0 |
added 439 characters in body
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| Nov 27, 2018 at 14:03 | history | edited | Claude Chaunier | CC BY-SA 4.0 |
added scores of Thue-Morse, reverse Thue-Morse and alternating sequences for n up to 17
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| Nov 27, 2018 at 6:44 | comment | added | Claude Chaunier | ok, I'll do it. I wonder if other weights than $0,1,\dots,n$ makes the Thue-Morse the fairest. | |
| Nov 27, 2018 at 6:43 | history | edited | Claude Chaunier | CC BY-SA 4.0 |
added n=14 and its fairest sequences
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| Nov 27, 2018 at 3:52 | comment | added | Harry Altman | Well, OK! If you're already planning to do more computation, do you mind if I ask you also: Just how close do Thue-Morse and reverse Thue-Morse come? Thanks! | |
| Nov 26, 2018 at 20:53 | history | edited | Claude Chaunier | CC BY-SA 4.0 |
added 535 characters in body
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| Nov 26, 2018 at 8:27 | comment | added | Claude Chaunier | @HarryAlman You may wait a few more days as well. And I'll improve on brute-force. Any consecutive run of $k$ random strikes could easily take $k!$ times less time. And computing upper and lower bounds on the values to expect after some binary prefix might help ruling it out before trying to lengthen it. | |
| Nov 26, 2018 at 6:02 | comment | added | Harry Altman | Thanks! Heh, guess I should've tried brute-forcing before asking; oh well. Anyway, this is interesting. Doesn't match TM or reverse TM unless $n\le 4$, it seems; it looks a little closer to reverse though? (For $n=3$, it matches that, but I could've told you that.) There's an obvious followup question here, which is "Is this always unique for $n$ odd?" -- but that's clearly a separate question. Anyway, going to wait a day to see if other answers, otherwise I'll accept this, because this does seem to answer my question. Meanwhile going to play around with this some. :) | |
| Nov 26, 2018 at 5:06 | history | edited | Claude Chaunier | CC BY-SA 4.0 |
increased $n$ to $11$
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| Nov 26, 2018 at 0:35 | history | answered | Claude Chaunier | CC BY-SA 4.0 |