2014/06/06 by Yann Bugeaud, Bugeaud, Yann, Guo-Niu Han +1
Computer Science · Mathematics · #05A05 #11J82 #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1406.1587
openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1998, Allouche, Peyrière, Wen and Wen established that the Hankel determinants associated with the Thue--Morse sequence on \-1, 1\ are always nonzero. Their proof depends on a set of sixteen recurrence relations. We present an alternative, purely combinatorial proof of the same result. We also re-prove a recent result of Coons on the non-vanishing of the Hankel determinants associated to two other classical integer sequences.