Uniformity in association schemes and coherent configurations: Cometric Q-antipodal schemes and linked systems

@article{Dam2013UniformityIA,
  title={Uniformity in association schemes and coherent configurations: Cometric Q-antipodal schemes and linked systems},
  author={Edwin R. van Dam and William J. Martin and Mikhail E. Muzychuk},
  journal={J. Comb. Theory, Ser. A},
  year={2013},
  volume={120},
  pages={1401-1439}
}
Inspired by some intriguing examples, we study uniform association schemes and uniform coherent configurations, including cometric Q-antipodal association schemes. After a review of imprimitivity, we show that an imprimitive association scheme is uniform if and only if it is dismantlable, and we cast these schemes in the broader context of certain — uniform — coherent configurations. We also give a third characterization of uniform schemes in terms of the Krein parameters, and derive… CONTINUE READING

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