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Volume 59, Issue 1

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

Nevena Francetić / Eric Mendelsohn
Published Online: 2009-01-08 | DOI: https://doi.org/10.2478/s12175-008-0110-3

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.

MSC: Primary 11B99, 05B07

Keywords: Skolem sequence; Langford sequence; design theory; triple systems; graph labeling; γ coverings

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About the article

Published Online: 2009-01-08

Published in Print: 2009-02-01


Citation Information: Mathematica Slovaca, Volume 59, Issue 1, Pages 39–76, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-008-0110-3.

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