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
4 Citations
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