Generalised Morse sequence

From Wikipedia, the free encyclopedia

To comply with Wikipedia's quality standards, this article may need to be rewritten. Reason: It never defines the subject. Many different generalizations have been studied according to sources. Please help improve this article. The discussion page may contain suggestions.

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:

Contents 1 Definition 1.1 Direct definition 1.2 Recurrence relation 1.3 L-system 1.4 Characterization using bitwise negation 1.5 Infinite product 2 Some properties 3 History 4 See also 5 External links

[edit] Definition

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

[edit] Direct definition

(to be done)

[edit] Recurrence relation

(to be done)

[edit] L-system

(to be done)

[edit] Characterization using bitwise negation

(to be done)

[edit] Infinite product

(to be done)

[edit] Some properties

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

[edit] History

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

[edit] See also

• Prouhet-Thue-Morse sequence

[edit] External links

• 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.