The symbol has symmetry properties with respect to permutation of columns, permutation of rows, and transposition of rows and columns; these relate 72 independent symbols. Even (cyclic) permutations of either columns or rows, as well as transpositions, leave the symbol unchanged. Odd permutations of columns or rows introduce a phase factor , where is the sum of all arguments of the symbol.
For recursion relations see Varshalovich et al. (1988, §10.5).
For generating functions for the symbol see Biedenharn and van Dam (1965, p. 258, eq. (4.37)).
This equation is the sum rule. It constitutes an addition theorem for the symbol.