Tiling With Three Element Sets

We consider tilings of intervals and other sets in \(\mathbb {Z}\) with translates of a three element integer set \(\mathcal {A}=\{0,a,a+b\}\) and its reflection \(\mathcal {B}=\{0,b,a+b\}.\) We also consider these questions for intervals and other sets in \(\mathbb {R}\) where a and b are real numbers.