An orderly algorithm and some applications in finite geometry Original Research Article

An algorithm for generating combinatorial structures is said to be an orderly algorithm if it produces precisely one representative of each isomorphism class. In this paper we describe a way to construct an orderly algorithm that is suitable for several common searching tasks in combinatorics. We illustrate this with examples of searches in finite geometry, and an extended application where we classify all the maximal partial flocks of the hyperbolic and elliptic quadrics in PG(3, q) for q ⩽ 13.