Abstract
Given integers a(1), a(2),...,a(n), with a(1)+ a(2) + ... + a(n) >= 1, a symmetrically constrained composition lambda(1) + lambda(2) + ... + lambda(n) = M of M into n nonnegative parts is one that satisfies each of the n! constraints {Sigma(n)(i=1) a(i)lambda(pi(i)) >= 0 : pi is an element of S-n}. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.