This paper deals with the question of completing a monotone increasing family of
subsets of a finite set
to obtain the linearly dependent subsets of a family of
vectors of a vector space. Specifically, we demonstrate that such vectorial completions
of the family of subsets ¿ exist and, in addition, we show that the minimal
vectorial completions of the family ¿ provide a decomposition of the clutter of the
inclusion-minimal elements of ¿. The computation of such vectorial decomposition
of clutters is also discussed in some cases.
CitacióMartí-Farré, J. Linearly dependent vectorial decomposition of clutters. "Electronic notes in discrete mathematics", 16 Setembre 2014, vol. 46, p. 209-216.