With Daniel Condon, Luke Serafin, and Cody Stockdale. Electronic journal of combinatorics, 2016. (arχiv | journal)

Abstract: 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.

Further info: This article represents a portion of the authors’ work during the 2014 math REU program at Boise State University.