A survey of Skolem-type sequences and Rosa's use of them

Abstract

Let D be a set of positive integers. A Skolem-type sequence is a sequence of i ∈ D such that every i ∈ D appears exactly twice in the sequence at positions ai and bi, and bi - ai = i. These sequences might contain empty positions, which are filled with null elements. Thoralf A. Skolem defined and studied Skolem sequences in order to generate solutions to Heffter's difference problems. Later, Skolem sequences were generalized in many ways to suit constructions of different combinatorial designs. Alexander Rosa made the use of these generalizations into a fine art. Here we give a survey of Skolem-type sequences and their applications. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009.