This paper deals with the question of completing a monotone increasing family of subsets to obtain the dependent sets of a matroid. More precisely, we provide several natural ways of transforming the clutter of the inclusion minimal subsets of the family into the set of circuits of a matroid.
Fàbrega, J.; Marti, J.; Muñoz, X. From clutters to matroids. A: Encuentro Andaluz de Matemática Discreta. "AVANCES EN MATEMÁTICA DISCRETA EN ANDALUCÍA - Volumen III". Sevilla: Universidad de Sevilla, 2013, p. 139-146.