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A283502
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Number of distinct subword complexity profiles for purely periodic binary infinite words of period n.
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0
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1, 2, 2, 4, 3, 7, 6, 13, 13, 23, 25, 47, 51, 87, 110, 176, 214, 342, 424, 676, 841, 1253, 1660
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OFFSET
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1,2
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COMMENTS
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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)).
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LINKS
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EXAMPLE
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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... .
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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