Explicit evaluations of the Hankel determinants of a Thue--Morse-like sequence

2014/06/06 by Guo-Niu Han, Wen Wu, Han, Guo-Niu +1
Chemistry · Computer Science · Mathematics · #05A15 #11B37 #11B85 #11C20 #15A15 #Advanced Combinatorial Mathematics #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1406.1594

openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain the explicit evaluations of the Hankel determinants of the formal power series ∏_{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 \0, ± 1, ± J, ± J²\. 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).

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