_{R_{j} } \left(\pi _{S} \right)$                                                                     A matrix of all coincidence set cardinalities for all input and output connections at $\pi _{S} $, defined as $Z_{R_{j} } \left(\pi _{S} \right)=Z_{R_{j} }^{\left(\pi _{S} \right)} \left(\left(R_{i} ,\sigma _{k} \right)\right)_{i\le N,k\le N} 