Premium
Overlap Cycles for Steiner Quadruple Systems
Author(s) -
Horan Victoria,
Hurlbert Glenn
Publication year - 2014
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.21378
Subject(s) - mathematics , steiner system , combinatorics , gray code , order (exchange) , discrete mathematics , set (abstract data type) , algorithm , computer science , economics , programming language , finance
Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v , or SQS( v ), exist if and only if v ≡ 2 , 4( mod 6 ) . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every v ≡ 2 , 4( mod 6 ) with v > 4 there exists an SQS( v ) that admits a 1‐overlap cycle.