Avoiding fractional powers on the alphabet N

Combinatorics on words is a relatively recent area of discrete mathematics, which finds its roots in the work of Axel Thue at the beginning of the 20th century. Avoidance of patterns is among the hottest topics in combinatorics on words. In this talk, I will focus on lexicographically least words on the alphabet of nonnegative integers avoiding some specific patterns called fractional powers.