On the Sum of the Heights of Sturmian Factors
Abstract
A binary word is a map W : N --> 0,1, and the set of factors of W with length n is Fn(W):=(W(i),W(i+1),...,W(i+n-1)) : i >= 0. A word is Sturmian if |Fn(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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