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 $\mathbf{p} \, \tau ( \varphi(\mathbf{z}) \varphi^2(\mathbf{z}) \cdots)$ where $\mathbf{p},\mathbf{z}$ are finite words, $\varphi$ 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.
@article{10_37236_9581,
author = {Eric Rowland and Manon Stipulanti},
title = {Avoiding 5/4-powers on the alphabet of nonnegative integers},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/9581},
zbl = {1460.68081},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9581/}
}
TY - JOUR
AU - Eric Rowland
AU - Manon Stipulanti
TI - Avoiding 5/4-powers on the alphabet of nonnegative integers
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/9581/
DO - 10.37236/9581
ID - 10_37236_9581
ER -
%0 Journal Article
%A Eric Rowland
%A Manon Stipulanti
%T Avoiding 5/4-powers on the alphabet of nonnegative integers
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/9581/
%R 10.37236/9581
%F 10_37236_9581
Eric Rowland; Manon Stipulanti. Avoiding 5/4-powers on the alphabet of nonnegative integers. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9581
