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On the uniqueness of embedding a residual design
Authors:Graham Kelly
Affiliation:Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164, USA
Abstract:We prove that if a residual 2-(k(k+λ?1)λ,k,λ) design R has more than one embedding into a symmetric design then k ? λ(λ?1)2. If equality holds then R has exactly two embeddings and the corresponding derived design is in both cases λ ? 1 identical copies of the design of points and lines of PG(3, λ ? 1). Using the main proposition from which these results follow we also prove that if a symmetric2-(v,k, λ) design has an axial non-central or central non-axial automorphism then k?λ(λ2 ? 2λ + 2).
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