Annals of Combinatorics 3 (1999) 27-35


Pooling, Lattice Square, and Union Jack Designs

Mark A. Chateauneuf1, Charles J. Colbourn2, Donald L. Kreher1, Esther R. Lamken3, and David C. Torney4

1Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931-1295, USA
 {machatea, Kreher}@mtu.edu

2Department of Computer Science, University of Vermont, Burlington, VT 05405, USA
 colbourn@emba.uvm.edu

3Department of Mathematics, 253-37, California Institute of Technology,Pasadena, CA 91125, USA
 lamken@cco.caltech.edu

4Theoretical Biology and Biophysics, T-10, MS K710, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
 dct@lanl.gov

Received January 18, 1999

AMS Subject Classification: 05B05

Abstract. Simplified pooling designs employ rows, columns, and principal diagonals from square and rectangular plates. The requirement that every two samples be tested together in exactly one pool leads to a novel combinatorial configuration: The union jack design. Existence of union jack designs is settled affirmatively whenever the order n is a prime and n ≡ 3 (mod 4).

Keywords: pooling design, affine plane, group testing


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