Talk:Thue-Morse sequence

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Mathematics rating: Start Class Low Priority  Field: Discrete mathematics

Hi,

(That's my 1st wikipedia entry so - my apologies if something is wrong...)

In the 'History' section, user 'colosimo' states:

'Also, the sequence was rediscovered in 2000 by 8th grade student John Colosimo, who used it as the perfect order in which participants in turn-taking games could most fairly take turns. It especially applies in games where the players move along a path to reach a desired goal, eliminating any advantage potentially gained by either player by taking the first turn.'

An interesting application for the Thue-Morse Sequence. Congratulations. However, I searched the web for an evidence of this statement without finding one. There are may other examples of people who 'happened' to re-discovered the Thue-Morse Sequence, so I suggest either to give an evidence (publication) that John Colosimo indeed re-discovered the Thue-Morse Sequence, or to delete the section.

Best regards

--80.171.178.236 16:23, 20 December 2006 (UTC) Janosch

\lim_{n\rightarrow \infin} a(n) is indeed balanced, though one must concede that most games consist of finite turns, and of those, most are predisposed to granting an unfair advantage to one side or the other, even when attempting to offset that advantage with Thue-Morse, due to the fact that the number of turns tends to most often fall in a fairly narrow band (which can be trivially proven by observing that in a game which typically finishes in a single turn, the first player will have a significant advantage!).
Even in situations where the number of turns is distributed in such a way that it offsets this advantage, many games still give undue benefit to the first player (for example, in Monopoly, if the best properties in the game were the light-blue properties—they aren't—which are available within a single move of the starting point, the first player would have the opportunity to land on such a property and claim it, whereas the second player would have a reduced chance to claim a light-blue property because one of the properties on which he might land has already been claimed). Nonetheless, the described reasoning is much the same as I employed when I discovered Thue-Morse at a very young age. It's worth noting that the first term of Thue-Morse must be discarded when you are attempting to use it to "balance" in this manner. Jouster  (whisper) 18:56, 28 November 2007 (UTC)

[edit] Image:Morse-Thue sequence.gif

Just FYI.--80.136.165.54 22:06, 8 July 2007 (UTC)

BTW: "Since Thue published in German, his work was ignored at first" is nonsense, Einstein also published in German. At that time, you could not just ignore Hilbert's publications because they were in German, or Poincaré's because they were French. (Actually, there is still quite a lot of mathematics being published in French.)--80.136.184.224 09:09, 9 July 2007 (UTC)