Extended skolem sequences

摘要

AbstractAk‐extended Skolem sequence of ordernis an integer sequence (s1, s2,…, s2n+1) in which sk= 0 and for eachjϵ {1,…,n}, there exists a unique i ϵ {1,…, 2n} such that si= si+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)kis 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. © 1995 John W