Abstract
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, Hobart [Mich. Math. J. 58:231–239, 2009] 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
