Let τ be the substitution 1 → 101 and 0 → 1 on the alphabet {0, 1}. The fixed point of τ leading by 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 Hm,n of s for all m ≥ 0 and n ≥ 1. Contents 1. Introduction 1 2. Some properties of the sequence s 3 3. Partition of the lattice 11 4. Relations of Hankel determinants 12 5. Evaluating the Hankel determinants 20 6. Proof of Theorem 1.1, 1.2 and 1.3 24 Acknowledgement 25 References 25
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.