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Extended skolem sequences

✍ Scribed by C. A. Baker

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
671 KB
Volume
3
Category
Article
ISSN
1063-8539

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✦ Synopsis

A k-extended Skolem sequence of order n is an integer sequence (s,, s2,. . . , S Z ~+ ~) in which sk = 0 and for eachj E (1,. . . ,n}, there exists a unique i E (1,. . . ,2n} such that si = s i + j = j .

We show that such a sequence exists if and only if either 1) k is odd and n = 0 or 1 (mod 4) or (2) k is even and n = 2 or 3 (mod 4). The same conditions are also shown to be necessary and sufficient for the existence of excess Skolem sequences. Finally, we use extended Skolem sequences to construct maximal cyclic partial triple systems.

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