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A combinatorial proof of the non-vanishing of Hankel determinants of the Thue--Morse sequence (1406.1587v1)
Published 6 Jun 2014 in math.CO and math.NT
Abstract: In 1998, Allouche, Peyri`ere, 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.