## Abstract

An n-color composition of n is a composition of n where a part κ has κ possible colors. It is known that the number of n-color compositions of n is F_{2n} (the 2nth Fibonacci numbers). Among other objects. F _{2n} 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 - 1 excluding 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.

Original language | American English |
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Journal | Fibonacci Quarterly |

Volume | 51 |

State | Published - May 1 2013 |

## Keywords

- Binary words
- Bisection
- Color compositinos
- Fibonacci numbers

## DC Disciplines

- Education
- Mathematics