Beyond the monomiality: the Monumbrality Principle

The monomiality principle has allowed the derivation, in a fairly straightforward way, of the properties of many families of special polynomials, recognized as quasi monomials. The family of quasi- monomials is large, but not all the special polynomials can be framed within this category. In this paper we will prove the existence of a larger family, including the quasi-monomials, by taking advantage from the umbral calculus and by introducing the concept of monum- brality, which appears very useful to get a deeper understanding in the nature and role of special polynomials.