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On the covering number $g_1^{(4)}(18)$

Grannell, Mike; Griggs, Terry; Stanton, R. G. and Whitehead, C. A. (2005). On the covering number $g_1^{(4)}(18)$. Utilitas Mathematica, 68, pp. 131–143.

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Abstract

The minimum number of blocks having maximum size precisely four that are required to cover, exactly $\lambda$ times, all pairs of elements from a set of cardinality $v$ is denoted by $g_{\lambda}^{(4)}(v)$. The values of $g_{\lambda}^{(4)}(v)$ are known apart from the cases $(v,\lambda)= (17,1)$ and $(18,1)$. We prove that $g_1^{(4)}(18)\ge 32$, thereby reducing this outstanding case to just two possible values, namely 32 and 33.

Item Type: Journal Article
ISSN: 0315-3681
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22771
Depositing User: Mike Grannell
Date Deposited: 18 Aug 2010 13:07
Last Modified: 07 Jan 2011 15:58
URI: http://oro.open.ac.uk/id/eprint/22771
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