Abstract
Arithmetical complexity of an infinite word, defined by Avgustinovich, Fon-Der-Flaass and Frid in 2000, is the number of words of length n which occur in its arithmetical subsequences. We present a construction of infinite words whose arithmetical complexity function grows faster than any polynomial, but slower than any exponential. Also we give a rough upper bound for the arithmetical complexity of the Sierpinski word.
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