# Ken W. Smith

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 Name Ken W. Smith Member for 2 years Seen 13 mins ago Website Location Huntsville, Texas, USA Age 58
I am a mathematics professor at Sam Houston State University, active in algebra & combinatorics and in directing undergraduate research.
 Dec28 answered Topics for an Undergraduate Expository Paper in Number Theory Dec27 comment 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. Dec27 answered Is there an infinite number of combinatorial designs with $r=\lambda^{2}$ Dec27 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