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Finiteness Results in Triangle-Free Quasi-Symmetric Designs

✍ Scribed by Rajendra M. Pawale

Book ID
112120497
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
507 KB
Volume
21
Category
Article
ISSN
1063-8539

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A~TRACT. The following result is proved: Let D be a quasi-symmetric 3-design with intersection numbers x, y(0 ~< x < y < k). D has no three distinct blocks such that any two of them intersect in x points if and only if D is a Hadamard 3-design, or D has a parameter set (v, k, 2

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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 β‰₯ 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 ≀ y( yx)+ x.