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Extended skolem sequences
Author(s) -
Baker C. A.
Publication year - 1995
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180030507
Subject(s) - mathematics , sequence (biology) , combinatorics , order (exchange) , integer (computer science) , mod , chemistry , computer science , biochemistry , finance , economics , programming language
A k ‐extended Skolem sequence of order n is an integer sequence (s 1 , s 2 ,…, s 2n+1 ) in which s k = 0 and for each j ϵ {1,…,n}, there exists a unique i ϵ {1,…, 2n} such that s i = 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. © 1995 John Wiley & Sons, Inc.