 $Z_{R_{j} }^{\left(\pi '_{S} \right)} \left(\left(R_{i} ,\sigma _{k} \right)\right)$                    Cardinality of the coincidence set ${\rm {\mathcal S}}_{R_{j} }^{\left(\pi _{S} \right)} \left(\left(R_{i} ,\sigma _{k} \right)\right)$ 