Geodesic
A combinatorial proof of the non-vanishing of Hankel determinants of the Thue-Morse sequence
The electronic journal of combinatorics, Tome 21 (2014) no. 3

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Zbl arXiv
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.
DOI : 10.37236/3831
Classification : 05A05, 11J82, 11B85
Mots-clés : Hankel determinant, combinatorial proof, Thue-Morse sequence 
Yann Bugeaud; Guo-Niu Han. A combinatorial proof of the non-vanishing of Hankel determinants of the Thue-Morse sequence. The electronic journal of combinatorics, Tome 21 (2014) no. 3. doi: 10.37236/3831
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     author = {Yann Bugeaud and Guo-Niu Han},
     title = {A combinatorial proof of the non-vanishing of {Hankel} determinants of the {Thue-Morse} sequence},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {3},
     doi = {10.37236/3831},
     zbl = {1298.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3831/}
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