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> What is the reason why there are 92 elements in this mathematical method Those elements are necessary and sufficient for closure in exactly the weird formal
by robot-wrangler 11mo ago
> What is the reason why there are 92 elements in this mathematical method
Those elements are necessary and sufficient for closure in exactly the weird formal automaton that the informal look-and-say sequence describes, i.e. once you have a graph and transition-states spelled out this much, there's just nowhere else for sequences to transition to. This would maybe be an unsatisfying answer except.. it's surprising at first that it's even finite, or for that matter that you can even analyze this kind of question in the first place.
They proved it originally by simplifying the cases that had to be examined, then enumerating stuff manually. All of which was probably so ugly and error-prone that it's no wonder several versions of the proof were "lost" ;) But later confirmed independently with code in various ways.. see the thing I linked elsewhere in thread. Or here's some work using haskell: https://www.cs.cmu.edu/~kw/pubs/conway.pdf https://www.cs.cmu.edu/~kw/pubs/conway.pdf
So besides graphs and transitions, number of elements is ultimately implied by the number base and the sequence rules (like reading left to right). Someone tried roman numerals but I can't find details. Ternary gives 24 elements apparently: https://arxiv.org/pdf/2405.11103 https://arxiv.org/pdf/2405.11103