2019/07/01 by Postic, Mickaël, Zamboni, Luca Q.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1907.01072
Let \A be a finite non-empty set and \preceq a total order on \A^\nats verifying the following lexicographic like condition: For each n∈ \nats and u, v∈ \An, if uω\prec vω then ux\prec vy for all x, y ∈ \A^\nats. A word x∈ \A^\nats is called ω-Lyndon if x\prec y for each proper suffix y of x. A finite word w∈ \A+ is called ω-Lyndon if wω\prec vω for each proper suffix v of w. In this note we prove that every infinite word may be written uniquely as a non-increasing product of ω-Lyndon words.