# §34.7 Basic Properties: Symbol

34.7.1

## §34.7(ii) Symmetry

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 further symmetry properties of the symbol see Edmonds (1974, pp. 102–103) and Varshalovich et al. (1988, §10.4.1).

## §34.7(iii) Recursion Relations

For recursion relations see Varshalovich et al. (1988, §10.5).

## §34.7(v) Generating Functions

For generating functions for the symbol see Biedenharn and van Dam (1965, p. 258, eq. (4.37)).

## §34.7(vi) Sums

34.7.3

This equation is the sum rule. It constitutes an addition theorem for the symbol.

34.7.5