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Ars Combinatoria

  • Research article

More on Exact Bicoverings of \(12\) Points

M.J. Grannell1, T.S. Griggs1, K.A.S. Quinn1, B.M. Maenhaut2, R.G. Stanton3
1Pure Mathematics Department The Open University, Walton Hall Milton Keynes, MIX7 6AA United Kingdom
2Department of Mathematics University of Queensland QLD, 4072, Australia
3Department of Computer Science University of Manitoba Winnipeg, Manitoba, R3T 2N2 Canada.
  • Published: 31/10/2003

Abstract

The minimum number of incomplete blocks required to cover, exactly \(A\) times, all \(t\)-element subsets from a set \(V\) of cardinality \(v\) (\(v \geq t\)) is denoted by \(g(\lambda,t;v)\). The value of \(g(2,2;v)\) is known for \(v = 3, 4, \ldots, 11\). It was previously known that \(14 \leq g(2, 2; 12) \leq 16\). We prove that \(g(2,2;12) \geq 15\).

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Citation
M.J. Grannell, T.S. Griggs, K.A.S. Quinn, B.M. Maenhaut, R.G. Stanton. More on Exact Bicoverings of \(12\) Points[J], Ars Combinatoria, Volume 069. 197-213. .