Ken W. Smith
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Registered User
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I am a mathematics professor at Sam Houston State University, active in algebra & combinatorics and in directing undergraduate research.
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Dec 28 |
answered | Topics for an Undergraduate Expository Paper in Number Theory |
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Dec 27 |
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Is there an infinite number of combinatorial designs with $r=\lambda^{2}$ @Felix: thanks! -- your more general question is probably VERY open! btw, even if a symmetric design does not exist (such as $(211,36,6)$), there is still a possibility that a design exists with the residual parameters. |
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Dec 27 |
answered | Is there an infinite number of combinatorial designs with $r=\lambda^{2}$ |
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Dec 27 |
comment |
Is there an infinite number of combinatorial designs with $r=\lambda^{2}$ If we restrict the question just to symmetric designs (so that $v=b$) then there are examples $(7,4,2), (25,9,3), (61,16,4),(121,25,5)$ described in the CRC Handbook of Combinatorial Designs [link text][1] (The list does not go far enough to examine $\lambda=6$.) If one removes a block from such a design one obtains a residual design in which $r$ is still equal to $\lambda^2.$ So there are certainly a number of examples. It would be interesting to know if there are any infinite families. [1]: emba.uvm.edu/~jdinitz/hcd.html |
