Critical exponents of infinite balanced words
Abstract
Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + root2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + root5)/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.
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Narad Rampersad, Jeffrey Shallit, Élise Vandomme
(2019).
Critical exponents of infinite balanced words. UWSpace.
http://hdl.handle.net/10012/15702
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