Nabil Shalaby - Skolem sequences: survey and new results

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Nabil Shalaby - Skolem sequences: survey and new results

	NABIL SHALABY, Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C 5S7, Canada
	Skolem sequences: survey and new results

A Skolem sequence of order n is a sequence $S = (s_1, s_2,\dots,s_{2n})$ of 2n integers satisfying the conditions:

1. for every $k\in \{1,2,\dots,n\}$ , there exist exactly two elements $s_i, s_j \in S$ such that s_i =s_j =k.

2. if s_i = s_j with i < j, then j - i = k.

It is well known that Skolem sequences link several combinatorial objects e.g. Steiner triple systems, Room squares and graph factorizations. We survey several known results and introduce some new applications of Skolem sequences to combinatorial designs and graph factorizations.

eo@camel.math.ca