Avoiding conjugacy classes on the 5-letter alphabet

11/20/2018

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by   Golnaz Badkobeh, et al.

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We construct an infinite word w over the 5-letter alphabet such that for every factor f of w of length at least two, there exists a cyclic permutation of f that is not a factor of w. In other words, w does not contain a non-trivial conjugacy class. This proves the conjecture in Gamard et al. [TCS 2018]