(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Izhakian, Zur; Rhodes, John
We extend the notion of matroid representations by matrices over fields by considering
new representations of matroids by matrices over finite semirings, more precisely over the boolean and
the superboolean semirings. This idea of representations is naturally generalized to include hereditary
collections (also known as abstract simplicial complexes). We show that a matroid that can be directly
decomposed as matroids, each of which is representable over a field, has a boolean representation, and
more generally that any arbitrary hereditary collection is superboolean-representable.
