Evaluations of the Hankel determinants of a Thue–Morse-like sequence

Guo-Niu Han (1) , Wen Wu (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics

We obtain simple relations between the Hankel determinants of the formal power series Q k≥0 (1 + Jx 3 k) where J = (√ −3 − 1)/2, and prove that the sequence of Hankel determinants is an aperiodic automatic sequence taking value in {±1, ±J, ±J 2 }. This research is essentially inspired by the works about Hankel determinants of Thue–Morse-like sequences by Allouche, Peyrière, Wen and Wen (1998), Bacher (2006) and the first author (2013). It is worth mentioning that we do not have a unified result, even though Bacher's result and ours are very similar.

Mots clés: Hankel determinant; Thue–Morse sequence; Thue–Morse-like sequence; automatic sequence; 11B37; 11B85; 11C20; 15A15

Domaines: Combinatoire [math.CO]

Guo-Niu Han, Wen Wu. Evaluations of the Hankel determinants of a Thue–Morse-like sequence. International Journal of Number Theory, 2015, 11 (6), ⟨10.1142/S1793042115500815⟩. ⟨hal-01278054⟩