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We have calculated S(q) and the single particle distribution function <n(q)>for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--sitelattice with periodic boundary conditions; we justify the use of this latticein compariosn to those of having the full square symmetry of the bulk. This newcluster has a high density of vec k points along the diagonal of reciprocalspace, viz. along k = (k,k). The results clearly demonstrate that when thesingle hole problem has a ground state with a system momentum of vec k =(pi/2,pi/2), the resulting ground state for N holes involves a shift of thepeak of the system's structure factor away from the antiferromagnetic state.This shift effectively increases continuously with N. When the single holeproblem has a ground state with a momentum that is not equal to k =(pi/2,pi/2), then the above--mentioned incommensurability for N holes is notfound. The results for the incommensurate ground states can be understood interms of rigid--band filling: the effective occupation of the single hole k =(pi/2,pi/2) states is demonstrated by the evaluation of the single particlemomentum distribution function <n(q)>. Unlike many previous studies, we showthat for the many hole ground state the occupied momentum states are indeed k =(+/- pi/2,+/- pi/2) states.Comment: Revtex 3.0; 23 pages, 1 table, and 13 figures, all include

Exact-diagonalization demonstration of incommensurability and the associated Fermi surface forNholes in thet-Jmodel