A hooked k-extended Skolem sequence of order n is a sequence s1s2…s2n+2 in which sk = s2n+1 = ε (ε is the null symbol) and each jϵ {1, 2, …, n} occurs exactly twice, the two occurrences separated by exactly j − 1 symbols. It is proved that, with the exception of (k, n) = (2, 1), such a sequence exists if and only if n ≡ 0, 1 (mod 4) for k even, and n ≡ 2, 3 (mod 4) for k odd. This result is then used to give an alternative proof of the existence of bicyclic Steiner triple systems.
Keywords
Designs
Skolem sequences
Langford sequences
Steiner triple systems
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Research supported by NSERC Operating Grant OGP0184169.