Flag algebras of symmetric design
If a symmetric design is either the point-hyperplane design of a projective space or the complement of a projective space over a field of order two then the algebra on the flags of the design has a natural extension to a seven-dimensional algebra of an association scheme. The purpose of this paper is to show that under certain additive conditions the converse is true, that is, if the flag algebra has an extension to seven-dimensional algebra of an association scheme then it is one of the designs mentioned above. The conditions are either \(\lambda\) divides k-1 or \(k=22\). The technical proofs use representation theory and counting argument to establish basic equations which imply the results.
scientific article; zbMATH DE number 4120179
scientific article