Rainbow cliques and the classification of small BLT-sets

Abstract

In Finite Geometry, a class of objects known as BLT-sets play an important role. They are points on the Q(4,q) quadric satisfying a condition on triples. This paper is a contribution to the difficult problem of classifying these sets up to isomorphism, i.e., up to the action of the automorphism group of the quadric. We reduce the classification problem of these sets to the problem of classifying rainbow cliques in graphs. This allows us to classify BLT-sets for all orders q in the range 31 to 67.