mmax

Mmax, written as mmax in some contexts, is a term that appears in mathematics, computer science, and data analysis as an informal shorthand for a maximum operation tied to a parameter or a collection of size m. Because it is not standardized, its exact meaning varies by author and domain.

In mathematics, mmax is often used to denote the maximum of a finite collection of elements or a function of a fixed size m. For example, mmax(S) may be read as max S for a finite set S. In statistics and order theory, the phrase “m-th maximum” (sometimes called the m-max) refers to the m-th largest value in a sample, a concept related to order statistics.

In computer science and programming, mmax frequently appears as a function name or operator that returns the largest value among m inputs. It can be implemented as a variadic function taking m arguments or as a function that computes the maximum over a collection of size m. In optimization, a related usage defines mmax_i f_i(x) = max{ f_i(x) : i = 1,...,m }, representing the maximum across m candidate functions.

Given its variety of uses, mmax is best understood through context. When encountered, one should consult the surrounding definitions to determine whether it denotes a simple maximum, an order statistic, or a maximum over a family of items or functions.

See also: max, order statistic, variadic function, and optimization.