EXTENDED LANGFORD SEQUENCES WITH SMALL DEFECTS

A k-extended Langford sequence of defect d and length m is a sequence s(1), s(2), ..., S2m + 1 in which s(k) = epsilon, where epsilon is the null symbol, and each other member of the sequence comes from the set {d, d + 1, ..., d + m - 1}. Each j is an element of {d, d + 1, ..., d + m - 1} occurs exactly twice in the sequence, and the two occurrence s are separated by exactly j - 1 symbols. In this paper wt prove that when d = 2, 3. the necessary conditions for the existence of such a se quence are sufficient. (C) 1998 Academic Press