The properties of the complexity function for finite words were studied in

M.-C. Anisiu, J. Cassaigne, Properties of the complexity function for finite words, Rev. Anal. Numer. Theor. Approx. 33 (2) (2004), 123-139. (citări ISI, alte citări).

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.