The Minor inequalities in the description of the Set Covering Polyhedron of Circulant Matrices

In this work we give a complete description of the set covering polyhedron of circulant matrices $C^k_{sk}$ with $s = 2,3$ and $k\geq 3 $ by linear inequalities. In particular, we prove that every non boolean facet defining inequality is associated with a circulant minor of the matrix. We also give a polynomial time separation algorithm for inequalities involved in the description.