Geodesic
On the Number of Associative Triples in an Algebra of n Elements
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 842-850

Voir la notice de l'article provenant de la source Cambridge University Press

Consider a set of n elements α1, ... , αn (denoted by S) and the set of all possible multiplication tables on these elements. The total number of such tables is clearly and each table can be represented by a square matrix [μij ] where μij is the product αiαj (μij ∈ S, i = 1, ... , n; j = 1, ... , n). The triple (αi, αj, αk) is said to be associative if the following equation is satisfied: 1.1 
Brockwell, P. J. On the Number of Associative Triples in an Algebra of n Elements. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 842-850. doi: 10.4153/CJM-1967-079-3
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[1] 1. Climescu, A. C., Etudes sur la théorie des systèmes multiplicatifs uniformes. I—L'indice de non-associativité, Bull. Ecole Polytech. Jassy, 2 (1947), 347–371. Google Scholar

[2] 2. Straus, E. G. and Wilf, H. S., Combinatorial aspects of the associative law of arithmetic (unpublished). Google Scholar

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