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Per en.wikipedia.org/wiki/N-ary_group Ternary associativity is (abc)de = a(bcd)e = ab(cde), i.e. the string abcde with any three adjacent elements bracketed. n-ary associativity is a string of length (n)+(n-1) with any n adjacent elements bracketed.
Hypermatrix multiplication of d-dimensional arrays with d-sides instead of left and right means an expression can be a tree of symbols instead of a line of symbols. Did Cayley consider hypermatrix multiplication?
