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Communication Dans Un Congrès Année : 2016

Computer assisted proof for Apwenian sequences related to Hankel determinants

Hao Fu
  • Fonction : Auteur
Guo-Niu Han

Résumé

An infinite ±1-sequence is called Apwenian if its Hankel determinant of order n divided by 2 n−1 is an odd number for every positive integer n. In 1998, Allouche,Peyrì ere, Wen and Wen discovered and proved that the Thue-Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han reproved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we find several new Apwenian sequences with Computer Assistance. This research has application in Number Theory to determining the irrationality exponents of some transcendental numbers.
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Dates et versions

hal-02125292 , version 1 (17-05-2019)

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Hao Fu, Guo-Niu Han. Computer assisted proof for Apwenian sequences related to Hankel determinants. International Symposium on Symbolic and Algebraic Computation, 2016, Waterloo, Canada. ⟨10.1145/2930889.2930891⟩. ⟨hal-02125292⟩
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