# Combinatorial representations

@article{Cameron2013CombinatorialR, title={Combinatorial representations}, author={Peter J. Cameron and Maximilien Gadouleau and S{\o}ren Riis}, journal={J. Comb. Theory, Ser. A}, year={2013}, volume={120}, pages={671-682} }

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… Expand

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