Generalised Morse sequence

Generalised Morse sequence

In mathematics and its applications, the Generalized Morse sequence, or Generalized Thue-Morse sequence, is a certain integer sequence. It has many properties of the binary Prouhet-Thue-Morse sequence and can thus be called its generalization:

Definition

There are several equivalent ways of defining the Generalized Morse sequence.

Direct definition

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Recurrence relation

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L-system

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Characterization using bitwise negation

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Infinite product

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Some properties

(to be done)Like the binary Thue-Morse Sequence, it answers the Prouhet-Tarry-Escott Problem.

History

The Generalized Morse Sequence was first described by Keynes in 1968.

See also

*Prouhet-Thue-Morse sequence

External links

* [http://www.cs.uwaterloo.ca/~shallit/Papers/ubiq.ps The Ubiquitous Prouhet-Thue-Morse Sequence.] Allouche, J.-P.; Shallit, J. O. Many applications of the binary Thue-Morse Sequence, and a chapter about the Generalized Morse Sequence - including the many properties of the binary sequence which are also found in the generalized one.


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