TITLE: 0-1 matrix corresponding to an abstract simplicial complex
QUESTION [6 upvotes]: Let $A$ be a 0-1 matrix whose columns are maximal. We can associate its rows with vertices and columns with simplices in an abstract simplicial complex. Conversely, given an ASC, we can encode it in a 0-1 matrix.
What is the name of this matrix? Surely it must be used in the literature, but I can't seem to find an instance.

REPLY [2 votes]: This looks like the incidence matrix of a clutter or hypergraph (whose edges are precisely the facets of your complex). It shows up quite a bit in optimization and combinatorial commutative algebra. For example see this question  for some interesting conjectures. If you are interested in this area, the key words are: max-flow min-cut, packing problem, facet ideals, etc.