On generalizations of separating and splitting families (Q311557)

Summary: Starting from the well-established notion of a separating family (or separating system) and the refinement known as a splitting family, we define and study generalizations called \(n\)-separating and \(n\)-splitting families, obtaining lower and upper bounds on their minimum sizes. For \(n\)-separating families our bounds are asymptotically tight within a linear factor, while for \(n\)-splitting families we provide partial results and open questions.