N-ary associativity
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In
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
, ''n''-ary associativity is a
generalization A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common character ...
of the
associative law In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ...
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..


References

Properties of binary operations {{algebra-stub