An algebraic integer q is a *PV number* (for Pisot-Vijayaraghavan number), if all its algebraic conjugates (except its complex conjugate, if `$q$`

is complex) are less than one in modulus. A profound theorem by Meyer states essentially, that a substitution tiling can only be a model set, if the inflation factor is a PV number [Mey95]
.

[Mey95]

Meyer, Y

**Quasicrystals, Diophantine approximation and algebraic numbers**

*Beyond quasicrystals (Les Houches, 1994), Springer, Berlin*
1995,
MR1420415