N-ary associativity

In algebra, $n$-ary associativity is a generalization of the associative law to $n$-ary operations.

A ternary operation is ternary associative if one has always
 * $$(abc)de=a(bcd)e=ab(cde);$$

that is, the operation gives the same result when any three adjacent elements are bracketed inside a sequence of five operands.

Similarly, an $n$-ary operation is $n$-ary associative if bracketing any $n$ adjacent elements in a sequence of $n + (n − 1)$ operands do not change the result.