Complementary Equations and Wythoff Sequences

  title={Complementary Equations and Wythoff Sequences},
  author={Clark Kimberling},
The lower Wythoff sequence a = (a(n)) and upper Wythoff sequence b = (b(n)) are solutions of many complementary equations f(a, b) = 0. Typically, f(a, b) involves composites such as a(a(n)) and a(b(n)), and each such sequence is treated as a binary word (e.g., aa and ab). Conversely, each word represents a sequence and, as such, is a linear combination of a, b, and 1, in which the coefficients of a and b are consecutive Fibonacci numbers. For example, baba = 3a + 5b − 6. 

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Complementary systems of integers

A. S. Fraenkel
Amer. Math. Monthly 84 • 1977

The bracket function and complementary sets of integers

A. S. Fraenkel
Canad. J. Math. 21 • 1969


E. Weisstein . 7 2000 Mathematics Subject Classification: Primary 11B37. Keywords: complementary equation, complementary sequences, Fibonacci numbers, golden ratio, Wythoff array, Wythoff sequence. • 1348
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