Distances of group tables and latin squares via equilateral triangle dissections

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 Drapal, Cavenagh and Wanless states that there exists c > 0 such that gdist(p) clog(p).

In this paper the conjecture is proved for c approximate to 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 5 log(2)(n) integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p) approximate to 3.56 for large values of p. (C) 2013 Elsevier Inc.

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Keywords

• Dissection Equilateral triangle
• Group table
• Latin square
• Plastic constant