Category:Definitions/Fibonacci Strings

This category contains definitions related to Fibonacci Strings.
Related results can be found in Category:Fibonacci Strings.

Consider the alphabet $\set {\text a, \text b}$.

For all $n \in \Z_{>0}$, let $S_n$ be the (finite) string formed as:

$S_n = \begin {cases} \text a & : n = 1 \\ \text b & : n = 2 \\ S_{n - 1} S_{n - 2} & : n > 2 \end{cases}$

where $S_{n - 1} S_{n - 2}$ denotes that $S_{n - 1}$ and $S_{n - 2}$ are concatenated.

The terms of the sequence $\sequence {S_n}$ are Fibonacci strings.