Thwarts in transversal designs |
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| Authors: | Charles J. Colbourn Jeffrey H. Dinitz Mieczyslaw Wojtas |
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| Affiliation: | (1) Combinatorics and Optimization, University of Waterloo, N2L 3G1 Waterloo, Ontario, Canada;(2) Mathematics, University of Vermont, 05405 Burlington, Vermont, USA;(3) Institute of Mathematics, Technical University of Wroclaw, Wroclaw, Poland |
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| Abstract: | A subset of points in a transversal design is athwart if each block in the design has one of a small number of intersection sizes with the subset. Applications to the construction of mutually orthogonal latin squares are given. One particular case involves inequalities for the minimum number of distinct symbols appearing in an  × subarray of an×n latin square. Using thwarts, new transversal designs are determined for orders 408, 560, 600, 792, 856, 1046, 1059, 1368, 2164, 2328, 2424, 3288, 3448, 3960, 3992, 3994, 4025, 4056, 4824, 5496, 6264, 7768, 7800, 8096, and 9336. |
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