Some remarks on subdesigns of symmetric designs |
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Authors: | Willem Haemers Mohan Shrikhande |
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Institution: | Technological University, Eindhoven, The Netherlands;Southern Illinois University, Carbondale, IL, U.S.A. |
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Abstract: | Let D(υ, k, λ) be a symmetric design containing a symmetric design D1(υ1, k1, λ1) (k1 < k) and let x = υ1(k ? k1)/(υ ? υ1). We show that k ≥(k1 ? x)2 + λ If equality holds, D1 is called a tight subdesign of D. In the special case, λ1 = λ, the inequality reduces to that of R.C. Bose and S.S. Shrikhande and tight subdesigns then correspond to their notion of Baer subdesigns. The possibilities for (7upsi;, k, λ) designs having Baer subdesigns are investigated. |
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Keywords: | Primary 05B05 Symmetric Design Subdesign Baer Subdesign Eigenvalues |
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