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On the Sum of the Heights of Sturmian Factors

Kevin O'Bryant
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Abstract

A binary word is a map W : N --> {0,1}, and the set of factors of W with length n is F_n(W):={(W(i),W(i+1),...,W(i+n-1)) : i >= 0}. A word is Sturmian if |F_n(W)|=n+1 for every n>0. We show that the sum of the heights (also known as hamming weights) of the n+1 factors with length n of a binary Sturmian word has the same parity as n, independent of W.

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Kevin O'Bryant. 2006-11-13. On the Sum of the Heights of Sturmian Factors. https://arxiv.org/abs/math/0611365

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