Geodesic
Tightness in subset bounds for coherent configurations
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 647-658.

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Association schemes have many applications to the study of designs, codes, and geometries and are well studied. Coherent configurations are a natural generalization of association schemes, however, analogous applications have yet to be fully explored. Recently, S. Hobart [Mich. Math. J. 58, No. 1, 231--239 (2009; Zbl 1285.05179)] generalized the linear programming bound for association schemes, showing that a subset $Y$ of a coherent configuration determines positive semidefinite matrices, which can be used to constrain certain properties of the subset. The bounds are tight when one of these matrices is singular, and in this paper we show that this gives information on the relations between $Y$ and any other subset. We apply this result to sets of nonincident points and lines in coherent configurations determined by projective planes (where the points of the subset correspond to a maximal arc) and partial geometries.
Classification : 05E30
Keywords: coherent configuration, Delsarte bound, finite geometry, association scheme 
@article{JAC_2014__39_3_a6,
     author = {Hobart, Sylvia A. and Williford, Jason},
     title = {Tightness in subset bounds for coherent configurations},
     journal = {Journal of Algebraic Combinatorics},
     pages = {647--658},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2014__39_3_a6/}
}
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Hobart, Sylvia A.; Williford, Jason. Tightness in subset bounds for coherent configurations. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 647-658. http://geodesic.mathdoc.fr/item/JAC_2014__39_3_a6/