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The concept of the reduced set of contact maps is introduced. Using this concept we find the ground state candidates for Hydrophobic-Polar lattice model on a two dimensional square lattice. Using these results we exactly enumerate the native states of all proteins for a wide range of energy parameters. In this way, we show that there are some sequences, which have an absolute native state. Moreover, we study the scale-dependence of the number of the members of the reduced set, the number of ground state candidates, and the number of perfectly stable sequences by comparing the results for sequences with lengths of 6 up to 20.
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