The properties of the complexity function for finite words were studied in
New definitions of maximal complexity were given and the number of words of a certain length for which that complexity is attained was calculated in
M.-C. Anisiu, Z. Blazsik, Z. Kasa, Maximal complexity of finite words, Publ. Math. Appl. 13 (1-2) (2002), 39-48. (citări)
Results on palindromic complexity were obtained in
M.-C. Anisiu, V. Anisiu, Z. Kasa, On the total palindrome complexity, Discrete Mathematics v. 310 (2010) no. 1, 109-114.