OFFSET
1,2
COMMENTS
The subword complexity function p_i(x) maps i to the number of distinct contiguous blocks (aka subwords, aka factors) of length i in an infinite word x. The subword complexity profile of an infinite word x is the infinite list (p_1 (x), p_2 (x), p_3 (x), ...). For a purely periodic infinite word x, of period n, it suffices to consider the finite list (p_1 (x), p_2 (x), ..., p_n (x)). Furthermore, if x = www... with w of length n, it suffices to consider the list (p_1 (ww), p_2 (ww), ..., p_n (ww)).
EXAMPLE
For period n = 5, there are exactly three distinct subword complexity profiles: (1,1,1,...) corresponding to the word 000...; (2,3,4,5,5,5,...) corresponding to the word 000010000100001...; and
(2,4,5,5,5,...) corresponding to the word 000110001100011... .
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Mar 09 2017
STATUS
approved