Suppose you have two unary operators $!$ being the factorial and $\partial_1$ being the partial derivative of a function w.r.t. its first parameter.
$$ n!m $$ $$ f \partial_1 g $$
The $!$ operator operates on an argument on its left side ($n$), whereas $\partial_1$ operates on its right side ($g$). Associativity comes to mind but it doesn't quite capture the property. What do we call the differing properties of both operators?
In $n!$, $!$ is called a postfix operator. $\partial_1$ in $\partial_1 g$ is called a prefix operator.