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On Singular 1-Rotational Steiner 2-Designs

✍ Scribed by Marco Buratti; Fulvio Zuanni

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 128 KB
Volume: 86
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2938

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✦ Synopsis

A Steiner 2-design is 1-rotational over a group G if it admits G as an automorphism group fixing one point and acting regularly on the remainder. 1-rotational Steiner 2-designs have come into fashion since 1981, when Phelps and Rosa (Discrete Math. 33 (1981), 57 66) studied Steiner triple systems that are 1-rotational over the cyclic group. While all 1-rotational Steiner 2-designs constructed in the past have exactly one short block-orbit, in this paper we also consider 1-rotational Steiner 2-designs not having this property. We call them singular and we show that they are quite rare. In particular, we enumerate all the abelian 1-rotational 2-(49, 4, 1) designs.

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