On the study of protein folding, our understanding about the protein
structures is limited. In this paper we find one way to characterize the
compact structures of lattice protein model. A quantity called Partnum is given
to each compact structure. The Partnum is compared with the concept
Designability of protein structures emerged recently. It is shown that the
highly designable structures have, on average, an atypical number of local
degree of freedom. The statistical property of Partnum and its dependence on
sequence length is also studied.Comment: 10 pages, 5 figure