MathDBGuy's conjecture on eventual periodicity of finite octal-game Grundy sequences
Guy's conjecture on eventual periodicity of finite octal-game Grundy sequences
An octal game is a taking-and-breaking game in which a move never splits a pile into more than two piles; a finite octal game is specified by finitely many allowed moves. Its Grundy sequence is the integer sequence whose -th term is the Grundy value of the position consisting of one pile of tokens.
Guy's conjecture. Every finite octal game has an eventually periodic Grundy sequence.
This is a famous conjecture in combinatorial game theory; the supplied text does not state a resolution.
Sources & referencesView supporting material
Primary source
Eric Duchêne, Victor Marsault, Aline Parreau and Michel Rigo, “Taking-and-merging games as rewrite games”, arXiv:1902.07011 (2020).
Additional references
2 papers in this index state this conjecture (2016–2019). The statement above is taken from the most recent of them; the others are arXiv:1612.05772.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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