The Penney's Game with Group Action

The Penney's Game with Group Action

Abstract Consider equipping an alphabet $$\mathcal {A}$$ 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 pa...

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Bibliographic Details
Main Authors: Li, Sean (Author), Khovanova, Tanya (Author)
Format: Article
Language:English
Published: Springer International Publishing, 2022-04-13T12:58:47Z.
Subjects:
Article
Online Access:Get fulltext
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520 |a Abstract Consider equipping an alphabet $$\mathcal {A}$$ 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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