Timeline for Quantifying the sense in which the Thue-Morse sequence is the fairest turn taking algorithm
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 1, 2021 at 3:16 | comment | added | Gerry Myerson | There's a little bit about fairness at mathenchant.wordpress.com/2017/01/16/… Many more references at en.wikipedia.org/wiki/… | |
| Jun 1, 2021 at 3:05 | comment | added | Gerry Myerson | Thue-Morse also comes up in assigning positions to rowers in boats, see recursed.blogspot.com/2009/11/… and the links given there – it's physics, but it amounts to a balancing of zeros & ones in what might be thought of as a fair way. | |
| Jun 1, 2021 at 2:39 | comment | added | Richard Stanley | Essentially the same question appears at mathoverflow.net/questions/37276. | |
| Jun 1, 2021 at 0:10 | comment | added | Brian Hopkins | No, in your context, I'm looking at a finite number of bullets, $n$ each, so sequences of $2n$ bits. Just to have a setting where I can compute all possible sequences. | |
| May 31, 2021 at 23:58 | comment | added | Nate River | Just twice - once to correct a typo in the problem statement ($<$ instead of $>$), and once to make the partial order a little weaker. When you say 8 and 10, you mean $V^8$ and $V^10$ respectively? | |
| May 31, 2021 at 23:56 | comment | added | Brian Hopkins | I see that the question has been refined a few times. Trying to look at this computationally (for even $n$ with $n/2$ shots each) I get optimal sequences 1001, 100101, but 10010011 for 8, then back to the expected 1001010110 for 10 -- I'm not confident of the computations. Also, the partial order definition seems very strong, i.e., aren't lots of sequences incomparable? (By the way, I have run across these kind of sequences questions in the context of fair division of indivisible items between two parties.) | |
| May 31, 2021 at 23:25 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 31, 2021 at 23:13 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 31, 2021 at 21:23 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 31, 2021 at 9:59 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 31, 2021 at 9:51 | history | asked | Nate River | CC BY-SA 4.0 |