Hankel determinants of a Sturmian sequence

摘要

Let tau be the substitution 1 -> 101 and 0 -> 1 on the alphabet [0, 1). The fixed point of tau obtained starting from 1, denoted by s, is a Sturmian sequence. We first give a characterization of s using f-representation. Then we show that the distribution of zeros in the determinants induces a partition of integer lattices in the first quadrant. Combining those properties, we give the explicit values of the Hankel determinants H-m,H-n of s for all m >= 0 and n >= 1.

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