Complementary Equations and Wythoff Sequences
Department of Mathematics
University of Evansville
1800 Lincoln Avenue
Evansville, IN 47722
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.
Full version: pdf,
(Concerned with sequences
Received November 27 2007;
revised version received July 21 2008.
Published in Journal of Integer Sequences, August 3 2008.
Journal of Integer Sequences home page