Scaling properties of maximally compact chains

Scaling of the exact function for the number of intramolecular nonbonded co ntacts in a single maximally compact linear homopolymer on hypercubic latti ces is determined as a function of number N of monomers and dimension d. A representative maximally compact structure is designed and an exact recursi ve expression for the maximum number m(max) of contacts is derived from tha t design. The equivalent nonrecursive expression yields the asymptotic scal ing of m(max) as (d-1)N- dN(Delta) + 1, with Delta = (d-1)/d. Implications in polymer and protein studies are discussed. [S1063-651X(99)12405-X].