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Infinite classes of anti-mitre and 5-sparse Steiner triple systems

✍ Scribed by Yuichiro Fujiwara

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
135 KB
Volume
14
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class modulo 36. The third construction generates many infinite classes of anti‐mitre STSs in the remaining possible orders. As a consequence of these three constructions we can construct anti‐mitre systems for at least 13/14 of the admissible orders. For 5‐sparse STS(υ), we give a construction for υ  ≡ 1, 19 (mod 54) and υ  ≠ 109. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 237–250, 2006

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