Latin trades on three or four rows |
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Authors: | Richard Bean |
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Affiliation: | Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Islamic Republic of Iran |
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Abstract: | Latin trades are closely related to the problem of critical sets in Latin squares. We denote the cardinality of the smallest critical set in any Latin square of order n by scs(n). A consideration of Latin trades which consist of just two columns, two rows, or two elements establishes that scs(n)?n-1. We conjecture that a consideration of Latin trades on four rows may establish that scs(n)?2n-4. We look at various attempts to prove a conjecture of Cavenagh about such trades. The conjecture is proven computationally for values of n less than or equal to 9. In particular, we look at Latin squares based on the group table of Zn for small n and trades in three consecutive rows of such Latin squares. |
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Keywords: | Latin squares Latin trades Integer programming |
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