[en] We present a procedure for the generation of all rigid commensurate monolayer-surface structures of a given symmetry, up to a certain number of adsorbate particles, Nads, in the unit cell. It is shown that the minimum energy structures in each unit cell are related to a well-defined sequence of Fourier terms of the single-particle-surface potential. This fact allows the prediction of stable commensurate monolayer-surface structures with the only knowledge of Fourier coefficients of the atom-surface potential. The impact of the presented theory for theoretical and experimental determination of atomic and molecular monolayer ground states, as well as its extension to higher dimensions (i.e., for intercalated crystals), is discussed. © 2007 The American Physical Society.