n-ary associativity

In algebra, n-ary associativity is a generalization of the associative law to n-ary operations. 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.^[1]

References

1. Dudek, W.A. (2001), "On some old problems in n-ary groups", Quasigroups and Related Systems 8: 15–36.