Maximal complexity of finite words … Maximal complexity of finite words … Maximal
complexity of finite words," Pure Mathematics and Applications, Department of Mathematics,
Corvinus University of Budapest, vol. 13(1-2), pages 39-48. …

The subword complexity of a finite word $ w $ of length $ N $ is a function which associates
to each $ n\le N $ the number of all distinct subwords of $ w $ having the length $ n $. We
define the\emph {maximal complexity} C (w) as the maximum of the subword complexity for
$ n\in\{1, 2,..., N\} $, and the\emph {global maximal complexity} K (N) as the maximum of C
(w) for all words $ w $ of a fixed length $ N $ over a finite alphabet. By R (N) we will denote
the set of the values $ i $ for which there exits a word of length $ N $ having K (N) subwords …