  We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$
with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and
$a^\dag$ are boson annihilation and creation operators, satisfying
$[a,a^\dag]=1$. This consequently provides the solution for the exponential
$e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.
