Dilated Floor Functions That Commute

Abstract We determine all pairs of real numbers (α, β) such that the dilated floor functions ⌊αx⌋ and ⌊βx⌋ commute under composition, i.e., such that ⌊α⌊βx⌋⌋ = ⌊β⌊αx⌋⌋ holds for all real x.