@article{Song2022, 
author = {Haocong Song and Wen Wu},
title = {Hankel determinants of a Sturmian sequence},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {3},
pages = {4233-4265},
keywords = {Hankel determinants, Sturmian sequences},
url = {https://www.sciopen.com/article/10.3934/math.2022235},
doi = {10.3934/math.2022235},
abstract = {Let    τ be the substitution    1  →  101 and    0  →  1 on the alphabet    {  0  ,  1  }. The fixed point of    τ 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      ,      n       of              s       for all    m  ≥  0 and    n  ≥  1.}
}