The Young-Fibonacci lattice has a natural r-differential analogue for every positive integer r. These posets are lattices, and can be constructed by a variation of the reflection construction. In addition, the product of an and poset is always an (r + s)-differential poset. This construction also preserves the lattice property. It is not known for any r > 1 whether there are any r-differential lattices other than those that arise by taking products of the Young–Fibonacci lattices and Young's lattice.
