Matrix elements of SU(6) generators for baryons with arbitrary $N_c$ quarks in mixed symmetric states $[N_c- 1,1]$

We derive general analytic formulae for the matrix elements of the SU(6) generators for mixed symmetric $[N_c-1,1]$ spin-flavor states with an arbitrary number $N_c$ of quarks. They are relevant for baryon spectroscopy in the $1/N_c$ expansion method applied to light baryons and can be used to study excited states. In this way previous work on non-strange baryons can be extended to both non-strange and strange baryons.