Maximal sets of involutions
Irving Reiner · Transactions of the American Mathematical Society · 1955
IRVING REINER §1.Let U" denote the unimodular group consisting of all nXn integral matrices of determinant +1.An element WCUn is called an involution if W2 = I{n) (the w-rowed identity matrix).We shall consider abelian sets of involutions in Un of maximal size, and call such a set a maximal set.For a given involution WC Un, define N(W) to be the maximum number of involutions, all conjugate to W in Un, which can occur in a maximal set.Certainly N(W) depends only on the class of W in Un.We already know(x) that as x, y, and z range over all non-negative integers such that 2x-t-y+z = n, the matrix