Generalised Morse sequence
From Wikipedia, the free encyclopedia
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:
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[edit] Definition
There are several equivalent ways of defining the Generalized Morse sequence.
[edit] Direct definition
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[edit] Recurrence relation
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[edit] L-system
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[edit] Characterization using bitwise negation
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[edit] Infinite product
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[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
[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.
