[¦bərn‚sīd frō′bē·nē·əs ‚thir·əm] (mathematics) Pertaining to a group of permutations on a finite set, the theorem that the sum over all the permutations, g, of the number of fixed points of g is equal to the product of the number of distinct orbits with respect to the group and the number of permutations in the group.