Extending symmetric designs

P. J. Cameron

doi:10.1016/0097-3165(73)90023-X

Extending symmetric designs

P. J. Cameron^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ² + 4λ + 2), k = λ² + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.

Original language	English
Pages (from-to)	215-220
Number of pages	6
Journal	Journal of Combinatorial Theory, Series A
Volume	14
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(73)90023-X
Publication status	Published - 1 Jan 1973

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title = "Extending symmetric designs",

abstract = "If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.",

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N2 - If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.

AB - If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.

UR - https://www.scopus.com/pages/publications/0041744324

U2 - 10.1016/0097-3165(73)90023-X

DO - 10.1016/0097-3165(73)90023-X

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AN - SCOPUS:0041744324

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VL - 14

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JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 2

ER -

Extending symmetric designs

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