Geodesic
Aperiodic subtraction games
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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Periodicity is a fundamental property of many combinatorial games. It is sought vigorously, yet remains elusive in important cases, such as for some octal games, notably Grundy's game. Periodicity is important, because it provides poly-time winning strategies for many games. In particular, subtraction games, impartial and partizan, have been proved to be periodic. Our main purpose here is to exhibit constructively a class of subtraction games which is demonstratively aperiodic and yet is shown to have linear-time winning strategies.
DOI : 10.37236/2015
Classification : 91A46, 91A05, 11B75, 68Q25
Mots-clés : combinatorial games, complementary sequences, numeration systems, complexity, aperiodicity 
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     author = {Aviezri S. Fraenkel},
     title = {Aperiodic subtraction games},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {2},
     doi = {10.37236/2015},
     zbl = {1237.91061},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2015/}
}
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Aviezri S. Fraenkel. Aperiodic subtraction games. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2015

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