科研之友
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摘要
A hooked Skolem sequence of order n is a sequence hS(n), = (s(1), s(2), . . . , s(2n+1)) of 2n + 1 integers containing each of the integers 1, 2, . . . , n exactly twice, such that two occurrences of the integer j is an element of {1, 2, . . . , n} are separated by exactly j - 1 integers, and s(2n) = 0. We prove that the necessary conditions are sufficient for the existence of two hooked Skolem sequences of order n with 0, 1, 2, . . . , n - 3 and n pairs in the same positions. Further, we apply this result to the fine structure of cyclic three-fold triple systems and cyclic four-fold triple systems for v equivalent to 13, 19 (mod 24). Then, we extend these results to the fine structure of cyclic directed triple systems and cyclic Mendelsohn triple systems.
- 出版日期2014-4-20
