  We prove that if a primitive and non-periodic substitution is injective on
initial letters, constant on final letters, and has Pisot inflation, then the
R-action on the corresponding tiling space has pure discrete spectrum. As a
consequence, all beta-substitutions for beta a Pisot simple Parry number have
tiling dynamical systems with pure discrete spectrum, as do the Pisot systems
arising, for example, from the Jacobi-Perron and Brun continued fraction
expansions.
