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Skolem sequences and additive permutations

✍ Scribed by Jaromir Abrham; Anton Kotzig

Publisher: Elsevier Science
Year: 1981
Tongue: English
Weight: 432 KB
Volume: 37
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90214-4

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✦ Synopsis

A new relation between extended C Wem sequences element) and additive permutations is presented.

(i.e., Skolem sequences with one zero Skolem [lOI has considered in connection with a study of some triple systems of Steiner' the following problem: is it possible to distribute the numbers 1, 2 , * -* 9 2n in n pairs (a,, b,) such that b, -a, = r for r = 1,2, . . . , n? A set of pairs of this kind is referred to as a '1, + 1 system.'

We zan now define Skolem sequence of size n to be any sequence x1, . . _ , x2,, of positive integers with the following properties:

(a) For any kE{l,..., n} there exist precisely two subscripts i(k), j(k) such that Xi(k) = Xi(k) = k.

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