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Quasi-symmetric designs and biplanes of characteristic three

โœ Scribed by S.S Sane; M.S Shrikhande


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
741 KB
Volume
60
Category
Article
ISSN
0097-3165

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The article is concerned with a characterization of quasi-symmetric (QS) designs with intersection numbers 0 and y. It uses the idea of a good block. Such a block G has the property that for any block B with IG n B J = y, every point is on a block containing G n B. It is proved that if a QS design I

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Quasi-symmetric triangle-free designs D with block intersection numbers 0 and y and with no three mutually disjoint blocks are studied. It is shown that the parameters of D are expressible in terms of only two parameters y and m, where m = k/y, k being the block size. Baartmans and Shrikhande prove

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Triangle-free quasi-symmetric 2-(v, k,k) designs with intersection numbers x, y; 01, are investigated. It is proved that k โ‰ฅ 2 yx -3. As a consequence it is seen that for fixed k, there are finitely many triangle-free quasi-symmetric designs. It is also proved that: k โ‰ค y( yx)+ x.

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Jungnickel and Tonchev conjectured in [4] that if a quasi-symmetric design D is an s-fold quasi-multiple of a symmetric (v,k, A) design with (k, (sl)A) = 1, then D is a multiple. We prove this conjecture under any one of the conditions: s 5 7, k -1 is prime, or the design D is a 3-design. It is show