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Author Munemasa, Akihiro ♦ Sawa, Masanori
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2009-10-14
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Combinatorics ♦ 05B05 ♦ 05E20 ♦ math
Abstract In this paper we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting abelian groups as point-regular automorphism groups. The resulting SQS has an extra property which we call A-reversibility, where A is the underlying abelian group. In particular, when A is a 2-group of exponent at most 4, it is shown that an A-reversible SQS always exists. When the Sylow 2-subgroup of A is cyclic, we give a necessary and sufficient condition for the existence of an A-reversible SQS, which is a generalization of a necessary and sufficient condition for the existence of a dihedral SQS by Piotrowski (1985). This enables one to construct A-reversible SQS for any abelian group A of order v such that for every prime divisor p of v there exists a dihedral SQS(2p).
Description Reference: J. Stat. Theory Practice 6 (2012), 97-128
Educational Use Research
Learning Resource Type Article
Page Count 31


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