(i) Given n pairs (x1, y1),..., (xn, yn), let G be the group of 2n permutations of the 2n variables which interchange xi and yi in all, some, or none of the n pairs. Let G0 be any subgroup of G, and let e be the number of elements in G0. Any element g ∈ G0 (except the identity)

is characterized by the numbers i1,...,ir (r ≥ 1) of the pairs in which xi and yi have been switched. Let di = yi − xi, and let δ(1) < ··· < δ(e−1), denote the ordered values (di1 + ··· + dir )/r corresponding to G0. Then

(5.71) continues to hold with e − 1 in place of M.

(ii) State the generalization of