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Disjoint skolem sequences and related disjoint structures
Author(s) -
Baker C.,
Shalaby N.
Publication year - 1993
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.3180010503
Subject(s) - disjoint sets , sequence (biology) , mathematics , combinatorics , order (exchange) , discrete mathematics , chemistry , biochemistry , finance , economics
Abstract A Skolem sequence of order n is a sequence S = (s 1 , s 2 …, s 2n ) of 2 n integers satisfying the following conditions: (1) for every k ∈ {1, 2,… n } there exist exactly two elements s i ,S j such that S i = S j = k ; (2) If s i = s j = k,i < j then j − i = k . In this article we show the existence of disjoint Skolem, disjoint hooked Skolem, and disjoint near‐Skolem sequences. Then we apply these concepts to the existence problems of disjoint cyclic Steiner and Mendelsohn triple systems and the existence of disjoint 1‐covering designs. © 1993 John Wiley & Sons, Inc.