@MISC{Nordh_np-completeness, author = {Gustav Nordh}, title = {N P-completeness of generalized multi Skolem sequences}, year = {} }

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Abstract

A Skolem sequence is a sequence a1,a2,...,a2n (where ai ∈ A = {1,...,n}), each ai occurs exactly twice in the sequence and the two occurrences are exactly ai positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = {1,...,n} are Skolem sets was solved by Thoralf Skolem [6] in 1957. Many generalizations of Skolem sequences have been studied. In this paper we prove that the existence question for generalized multi Skolem sequences is N P-complete. This can be seen as an upper bound on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. Key words: Skolem sequence, design theory, NP-completeness 1