The factor complexity 
of a finite or infinite word 
, also called its subword complexity, is the number of distinct
contiguous factors of length 
occurring in 
.
The Morse-Hedlund theorem states that a right-infinite word is ultimately periodic
if and only if 
for some positive integer 
. Consequently, an aperiodic right-infinite word has factor
complexity at least 
for every 
.
Sturmian sequences are precisely the aperiodic
binary words attaining 
.
Among ternary words with factor complexity 
, the minimum possible critical
exponent is 
(Currie 2026).
and Minimal Critical Exponent." Elec. J. Combin. 33, No. 3,
P3.31, 2026.