Mathematical Sciences: Faculty Publications
Binary Words, N-Color Compositions and Bisection of the Fibonacci Numbers
Document Type
Article
Publication Date
5-2013
Publication Title
Fibonacci Quarterly
ISSN
0015-0517
Abstract
An n-color composition of n is a composition of n where a part k has k possible colors. It is known that the number of n-color compositionsof n is F2n (the 2nth Fibonacci numbers). Among other objects,F2n also counts the number of binary words with exactly n−1 strictly increasing runs and the number of {0, 1, 2} strings of length n − 1excluding the subword 12. In this note, we show bijections between n-color compositions and these objects. In particular, the bijection between the n-color compositions and the binary words with n − 1 increasing substrings generalizes the classic bijection between compositions and binary words of length n − 1. We also comment on the potential applications of these findings.
Recommended Citation
Wang, Hua, Alex Collins, Charles Dedrickson.
2013.
"Binary Words, N-Color Compositions and Bisection of the Fibonacci Numbers."
Fibonacci Quarterly, 51 (2): 130-136.
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/214
Copyright
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