A characterization of symmetric block designs
نویسندگان
چکیده
منابع مشابه
On a Characterization of Symmetric Balanced Incomplete Block Designs
All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated...
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In his book [I 1, Marshall Hall gives a table of balanced incomplete block designs with from 3 to 15 replications. It is mentioned there that a solution is unknown as to whether or not there exists a symmetric block design with parameters (v, k, h) = (36, 15, 6) (number 104 in the table). It is the purpose of this paper to show that such a design can in fact be constructed quite simply and to s...
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Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...
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A quasi-symmetric design (QSD) is a (v, k, λ) design with two intersection numbers x, y, where 0 ≤ x < y < k. The block graph of a QSD is a strongly regular graph (SRG), whereas the converse is not true. Using Neumaier’s classification of SRGs related to the smallest eigenvalue, a complete parametric classification of QSDs whose block graph is an SRG with smallest eigenvalue −3, or second large...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1972
ISSN: 0097-3165
DOI: 10.1016/0097-3165(72)90045-3