Block-Transitive Point-Imprimitive t-Designs |
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Authors: | Avinoam Mann Ngo Dac Tuan |
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Affiliation: | (1) Einstein Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel;(2) Residence Universitaire La Pacaterie, Chambre 452 Rue de la Pacaterie, Orsay, 91400, France |
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Abstract: | We study block-transitive point-imprimitive t–(v, k, ) designs. It was showed by Cameron and Praeger that in such designs t = 2 or 3. In 1989, Delandtsheer and Doyen proved that a block-transitive point-imprimitive 2-design satisfies v ((k2)–1)2. In this paper, we give a proof of the Cameron–Praeger conjecture which states that for t = 3 the stronger inequality v (k2)+1 holds. We find two infinite families of 3-designs for which this bound is met. We also show that the above designs cannot have = 1, and that = 2 is possible only if v attains its maximal value, and various other restrictions are met. |
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Keywords: | t-designs block transitivity |
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