Duality in coherent configurations

Abstract

By introducing a duality operator in coherent algebras (i.e. adjacency algebras of coherent configurations) we give a new interpretation to Delsarte's duality theory for association schemes. In particular we show that nonnegative matrices and positive semidefinite matrices, (0, 1)-matrices and distance matrices, regular graphs and spherical 2-designs, distance regular graphs and Delsarte matricesare pairs of dual objects. Several “almost dual” properties which are not yet fully understood are also reported.

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Neumaier, A. Duality in coherent configurations. Combinatorica 9, 59–67 (1989). https://doi.org/10.1007/BF02122684

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AMS subject classification (1980)

  • 05B20
  • 05C50