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

On t-extensions of the Hankel determinants of certain automatic sequences

Abstract. In 1998, Allouche, Peyrière, Wen and Wen considered the Thue–Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integers. We speak of t-extension when the entries along the diagonal in the Hankel determinant are all multiplied by t. We prove that the t-extension of each Hankel determinant of the period-doubling sequence is a polynomial ...

Hankel determinants of the Thue-Morse sequence

Acoustic Wave propagation through multilayer Thue-Morse structures containing two, three and four materials of Cu, Al, MgO and Pb

In this paper, the acoustic wave propagation in multilayer Thue-Morse structures has theoretically been studied. The composing layers were assumed do be Cu, Al, Mgo and Pb materials. Two, three or four different materials have been used in a typical structure. By using a perpendicular incident acoustic wave, the transmission coefficient was calculated and then by its old, the frequency gaps was...

A New Proof of the Prouhet-tarry-escott Problem

The famous Prouhet-Tarry-Escott problem seeks collections of mutually disjoint sets of non-negative integers that have equal sums of like powers. In this paper we present a new proof of the solution to this problem by deriving a generalization of the product generating function formula for the classical Prouhet-Thue-Morse sequence.

Nonoverlap Property of the Thue-Morse Sequence

In this note, we provide a new proof for the nonoverlap property of the ThueMorse sequence using a Boolean functions approach and investigate other patterns that occur in a generalization of the Thue-Morse sequence.