Portal de Periódicos da CAPES

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

2009; Springer Science+Business Media; Volume: 59; Issue: 1 Linguagem: Inglês

10.2478/s12175-008-0110-3

1337-2211

Nevena Francetić, Eric Mendelsohn,

Mathematics and Applications

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 a i and b i, and |b i − a i| = 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.