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...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Springer International Publishing,
2022-04-13T12:58:47Z.
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Subjects: | |
Online Access: | Get fulltext |
Summary: | 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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