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arXiv · 2009.06080

The Penney's Game with Group Action

Tanya Khovanova·Sean Li
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Abstract

Consider equipping an alphabet $\mathcal{A}$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the 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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Tanya Khovanova, Sean Li. 2020-12-14. The Penney's Game with Group Action. https://doi.org/10.1007/s00026-021-00564-1

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