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arXiv · 1303.3421

The intersection spectrum of Skolem sequences and its applications to lambda fold cyclic triple systems, together with the Supplement

Nabil Shalaby·Daniela Silvesan
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Abstract

A Skolem sequence of order n is a sequence S_n=(s_{1},s_{2},...,s_{2n}) of 2n integers containing each of the integers 1,2,...,n exactly twice, such that two occurrences of the integer j in {1,2,...,n} are separated by exactly j-1 integers. We prove that the necessary conditions are sufficient for existence of two Skolem sequences of order n with 0,1,2,...,n-3 and n pairs in same positions. Further, we apply this result to the fine structure of cyclic two, three and four-fold triple systems, and also to the fine structure of lambda-fold directed triple systems and lambda-fold Mendelsohn triple systems. For a better understanding of the paper we added more details into a "Supplement".

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Nabil Shalaby, Daniela Silvesan. 2013-03-15. The intersection spectrum of Skolem sequences and its applications to lambda fold cyclic triple systems, together with the Supplement. https://doi.org/10.1016/j.disc.2012.03.018

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