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Some New Infinite Classes of Candelabra Quadruple Systems
Author(s) -
Zhang Shaopu,
Ji Lijun,
Song Guojie
Publication year - 2016
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.21409
Subject(s) - mathematics , generalization , combinatorics , group (periodic table) , discrete mathematics , mathematical analysis , organic chemistry , chemistry
Candelabra quadruple systems (CQS) were first introduced by Hanani who used them to determine the existence of Steiner quadruple systems. In this paper, a new method has been developed by constructing partial candelabra quadruple systems with odd group size, which is a generalization of the even cases, to complete a design. New results of candelabra quadruple systems have been obtained, i.e. we show that for any n ≥ 3 , there exists a CQS ( g n : s ) for all g ≡ 0 ( mod 6 ) , s ≡ 0 ( mod 2 ) , and s ≤ g .
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