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Sets of associative triples. (English) Zbl 0612.05003
Authors’ summary: ”A subset \(R\subseteq S^ 3\) will be called (associatively) admissible if there exists a binary operation * defined on S such that \(x*(y*z)=(x*y)*z\) iff (x,y,z)\(\in R\). If S is finite, \(card(S)=n\), \(R\subseteq S^ 3\), \(card(R)=r\) and \(r\leq n/4-3/4\) or \(n^ 3-n/4+1/2\leq r\), then R is admissible. There exists an admissible subset for any \(0\leq r\leq n^ 3\) and a non-admissible subset for 3n\(\leq r\leq n^ 3-n+2.\)”
Reviewer: K.Burian

MSC:
05A05 Permutations, words, matrices
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References:
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