A Combinatorial Proof of the Non-Vanishing of Hankel Determinants of the Thue-Morse Sequence

Yann Bugeaud, Guo-Niu Han


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.


Hankel determinant, combinatorial proof, Thue-Morse sequence

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