A Proof of the Jungnickel-Tonchev Conjecture on Quasi-Multiple Quasi-Symmetric Designs |
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Authors: | Sharad Sane |
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Affiliation: | (1) Department of Mathematics, University of Mumbai, Vidyanagari, Santa Cruz (East), Mumbai-, 400 098, India |
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Abstract: | A proof of the following conjecture of Jungnickel and Tonchev on quasi-multiple quasi-symmetric designs is given: Let D be a design whose parameter set (v,b,r,k,) equals (v,sv,sk,k, s) for some positive integer s and for some integers v,k, that satisfy (v-1) = k(k-1) (that is, these integers satisfy the parametric feasibility conditions for a symmetric (v,k,)-design). Further assume that D is a quasi-symmetric design, that is D has at most two block intersection numbers. If (k, (s-1)) = 1, then the only way D can be constructed is by taking multiple copies of a symmetric (v,k, )-design. |
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Keywords: | block intersection numbers symmetric designs quasi-symmetric designs quasi-multiples multiples proper quasi-multiple designs |
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