The abelian complexity of infinite words and the Frobenius problem
Abstract
We study the following problem, first introduced by Dekking. Consider an infinite word x over an alphabet 0,1,...,k-1 and a semigroup homomorphism S:0,1,...,k-1* -> N. Let Lx denote the set of factors of x. What conditions on S and the abelian complexity of x guarantee that S(Lx) contains all but finitely many elements of N? We examine this question for some specific infinite words x having different abelian complexity functions.
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