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We study the set covering polyhedron related to circulant matrices. Inparticular, our goal is to characterize the first Chv\'atal closure of theusual fractional relaxation. We present a family of valid inequalities thatgeneralizes the family of minor inequalities previously reported in theliterature and includes new facet-defining inequalities. Furthermore, wepropose a polynomial time separation algorithm for a particular subfamily ofthese inequalities.

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