Duals of Tirilman spaces have unique subsymmetric basic sequences

The Tirilman spaces $Ti(p,\gamma )$, $1<p<\mathrm{\infty }$, were introduced by Casazza and Shura as variations of the spaces constructed by Tzafriri. We prove that all subsymmetric basic sequences in the dual space $T{i}^{\ast }(p,\gamma )$ are equivalent to its canonical subsymmetic but not symmetric basis.