Definition:Parity Operator

Definition

The parity operator is a unary operator on the integers defined as:

$\forall n \in \Z: \paren {-1}^n$

There is no evolved notation for this, neither is there an accepted name for it.

Motivation

When assembling complicated sequences in which each term is constructed in the form of an algebraic expression, it is commonplace for a factor of the form $\paren {-1}^n$ to appear.

The term parity operator was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ in order to provide a compact way to refer to terms of the form $\paren {-1}^n$.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

There appears to be no evolved notation for this, neither is there an accepted name for it.