Repetition threshold for circular words
Summary: We find the threshold between avoidable and unavoidable repetitions in circular words over \(k\) letters for any \(k\geq6\). Namely, we show that the number CRT\((k)=\frac{\left\lceil {k/2}\right\rceil{+}1}{\left\lceil {k/2}\right\rceil}\) satisfies the following properties. For any \(n\) there exists a \(k\)-ary circular word of length \(n\) containing no repetition of exponent greater than CRT\((k)\). On the other hand, \(k\)-ary circular words of some lengths must have a repetition of exponent at least CRT\((k)\).
scientific article; zbMATH DE number 6171794