an:03989347
Zbl 0612.05003
Dr??pal, A.; Kepka, T.
Sets of associative triples
EN
Eur. J. Comb. 6, 227-231 (1985).
00150546
1985
j
05A05
admissible subset
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\(\leq r\leq n^ 3-n+2.\)''
K.Burian