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The Penney’s Game with Group Action

Abstract

Consider equipping an alphabet \(\mathcal {A}\) with a group action which partitions the set of words into equivalence classes which we call patterns. We answer standard questions for Penney’s game on patterns and show non-transitivity for the game on patterns as the length of the pattern tends to infinity. We also analyze bounds on the pattern-based Conway leading number and expected wait time, and further explore the game under the cyclic and symmetric group actions.

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Acknowledgements

We are grateful to the MIT PRIMES-USA program for giving us the opportunity to conduct this research. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Correspondence to Sean Li.

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Communicated by Ilse Fischer.

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Li, S., Khovanova, T. The Penney’s Game with Group Action. Ann. Comb. 26, 145–170 (2022). https://doi.org/10.1007/s00026-021-00564-1

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  • DOI: https://doi.org/10.1007/s00026-021-00564-1