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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 thecourse of these considerations we define and explore the monomiality principleand find its representations. We exploit the properties of Sheffer-typepolynomials which constitute the inherent structure of this problem. In the endwe give some examples illustrating the utility of the method and point out therelation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics  "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),  Myczkowce, Poland. 13 pages, 31 reference

Monomiality principle, Sheffer-type polynomials and the normal ordering problem