Dilated floor functions having nonnegative commutator I. Positive and mixed sign dilations

Jeffrey C. Lagarias, D. Harry Richman

In this paper and its sequel we classify the set $S$ of all real parameter pairs $(\alpha ,\beta )$ such that the dilated floor functions $f_{\alpha }(x)=\lfloor \alpha x\rfloor$ and $f_β(x) = \lfloor{β…