Mathematical Sciences Seminar - Combinatorial Representations
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
Combinatorial representations are a new concept and focus on dependence relations amongst functions. In a sense, they are generalisations of linear representations of matroids based on functions over an alphabet. In this talk, we define combinatorial representations of a family of bases (r-sets of an n-set). We first show that any family is representable by matrices over some finite alphabet. We then give a characterisation of families representable over a given alphabet as subgraphs of a determined hypergraph. If time permits, we finally show how the study of so-called rank functions can be used to characterise the representations. These results quantify how much information functions must give out in order to satisfy some independence constraints.
Contact name:
Department of Economics, Mathematics and Statistics