The lexicographically least square-free word with a given prefix

by   Siddharth Berera, et al.

The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix p is denoted L(p). When p is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence. For other prefixes, the structure is significantly more complicated. In this paper, we show that L(p) reflects the structure of the ruler sequence for several words p. We provide morphisms that generate L(n) for letters n=1 and n≥3, and L(p) for most families of two-letter words p.


page 1

page 2

page 3

page 4


No extremal square-free words over large alphabets

A word is square-free if it does not contain any square (a word of the f...

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

We identify the structure of the lexicographically least word avoiding 5...

Parikh Motivated Study on Repetitions in Words

We introduce the notion of general prints of a word, which is substantia...

Avoiding squares over words with lists of size three amongst four symbols

In 2007, Grytczuk conjecture that for any sequence (ℓ_i)_i≥1 of alphabet...

Walking on Words

Take any word over some alphabet. If it is non-empty, go to any position...

On the rigidity of Arnoux-Rauzy words

An infinite word generated by a substitution is rigid if all the substit...

Wake Word Detection Based on Res2Net

This letter proposes a new wake word detection system based on Res2Net. ...

Please sign up or login with your details

Forgot password? Click here to reset