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EnglishA 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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| Titolo: | On singular 1-rotational Steiner 2-designs |
| Autori: | |
| Data di pubblicazione: | 1999 |
| Rivista: | |
| Abstract: | 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. |
| Handle: | http://hdl.handle.net/11391/22766 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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