Fibonacci (p, r)-cubes as Cartesian products

The Fibonacci (p, r)-cube Γ(p,r)n is the subgraph of Qn induced on binary words of length n in which there are at most r consecutive ones and there are at least p zeros between two substrings of ones. These cubes simultaneously gen-eralize several interconnection networks, notably hypercubes, Fibonacci cubes, and postal networks. In this note it is proved that Γ (p,r) n is a non-trivial Carte