AxByOz

AxByOz is a symbolic notation that appears in mathematics and computer science more as a descriptive construct than as a widely recognized mathematical object. It is typically used to illustrate how a sequence of symbols or factors can be arranged in a fixed order, and it may function as either a product-like expression or a simple concatenated word.

One common interpretation treats AxByOz as the product of three factors arranged in a specific order: A·x · B·y · O·z. In this view, A, B, and O are constants or operators, while x, y, and z are variables or subsequent factors. In another interpretation, AxByOz is simply a six-character word formed by the alphabet {A, x, B, y, O, z}. This dual usage helps in teaching concepts such as order of operations, variable placement, and concatenation in formal languages.

For example, if A, B, and O are set to 1 and x, y, z to 2, the expression evaluates to 1·2·1·2·1·2 = 8. If the symbols represent noncommutative objects (such as matrices or linear operators), the order matters, and AxByOz may not equal BxAyOz.

In scholarly contexts, AxByOz serves as a notational example rather than a named mathematical object with a dedicated theory. It is used to discuss notation conventions, to illustrate patterns of concatenation, and to aid pedagogy in algebra, combinatorics, and computer science.

See also: Monomial, Concatenation, Formal language, Notation in mathematics.