Avoiding 5/4-powers on the alphabet of nonnegative integers

Abstract

We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $p\tau (\phi (z){\phi }^2(z)\cdots )$ where $p,z$ are finite words, $\phi$ is a 6-uniform morphism, and $\tau$ is a coding. This description yields a recurrence for the $i$th letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove $k$-regularity for a sequence satisfying a recurrence of the same type.

35 pages, 3 figures

References in corpus (2)

• Avoiding 3/2-powers over the natural numbers
• Avoiding fractional powers over the natural numbers