A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring.
Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$.
For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...
