  In our recent paper [Phys. Lett. B 753, (2016) 122], we have shown that both
the odd and even tensor electric transition probabilities exhibit similar
behavior within the generalized seniority scheme in a multi-j environment. This
microscopic approach was used to show for the first time the occurrence of
seniority isomers in the $ {13}^-$ isomers of Sn-isotopes, which decay by odd
tensor $E1$ transition to the same seniority ($\Delta v = 0$) state. In this
letter, we extend our studies to odd tensor $E3$ transitions connecting
different seniority states ($\Delta v = 2$), and show for the first time that
the generalized seniority scheme explains reasonably well the systematics of
the $B(E3)$ values for the $(0^+ \rightarrow 3_1^-)$ transitions in the
Sn-isotopes. Additionally, we support these results by seniority guided Large
Scale Shell Model (LSSM) calculations. The generalized seniority results are
able to single out the most crucial valence space required in the LSSM
calculations.
