Resolving a question of Banero, we show that for every integer K > 1, there exists a word with additive complexity identically K. This result is perhaps surprising in light of the rather strong restriction on the existence of words with constant abelian complexity, given in the work of Currie and Rampersad. To prove our result we generalize the notion of a sturmian word. We also pose some questions regarding the existence and structure of words with fixed additive complexity.
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