Generalized minor inequalities for the set covering polyhedron related to circulant matrices

We study the set covering polyhedron related to circulant matrices. In particular, our goal is to characterize the first Chv'atal closure of the usual fractional relaxation. We present a family of valid inequalities that generalizes the family of minor inequalities previously reported in the literature and includes new facet-defining inequalities. Furthermore, we propose a polynomial time separation algorithm for a particular subfamily of these inequalities.