Publication details for Dr Maximilien GadouleauCameron, Peter J., Gadouleau, Maximilien & Riis, Søren (2013). Combinatorial Representations. Journal of Combinatorial Theory, Series A 120(3): 671-682.
- Publication type: Journal Article
- ISSN/ISBN: 0097-3165
- DOI: 10.1016/j.jcta.2012.12.002
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then prove that any graph is representable over all alphabets of size larger than some number depending on the graph. We also provide a characterisation of families representable over a given alphabet. Then, we associate a rank function and a closure operator to any representation which help us determine some criteria for the functions used in a representation. While linearly representable matroids can be viewed as having representations via matrices with only one row, we conclude this paper by an investigation of representations via matrices with only two rows.