Distances of group tables and latin squares via equilateral triangle dissections |
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Authors: | Michal Szabados |
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Affiliation: | Department of Algebra, Charles University in Prague, Sokolovská 83, 186 75 Prague 8, Czech Republic |
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Abstract: | Denote by gdist(p) the least non-zero number of cells that have to be changed to get a latin square from the table of addition modulo p . A conjecture of Drápal, Cavenagh and Wanless states that there exists c>0 such that gdist(p)?clog(p). In this paper the conjecture is proved for c≈7.21, and as an intermediate result it is shown that an equilateral triangle of side n can be non-trivially dissected into at most 5log2(n) integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p)≈3.56 for large values of p. |
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Keywords: | Dissection Equilateral triangle Group table Latin square Plastic constant |
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