On the enumeration of restricted words over a finite alphabet

TL;DR

This paper introduces a systematic method for counting restricted words over finite alphabets using invert transforms and partial Bell polynomials, generalizing previous enumeration techniques.

Contribution

It presents a novel approach that unifies and extends existing methods for enumerating restricted words through mathematical transforms.

Findings

Provides a general framework for enumeration of restricted words

Utilizes invert transform and Bell polynomials for systematic counting

Extends previous results in word enumeration

Abstract

We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which relies on the invert transform and its representation in terms of partial Bell polynomials, allows us to generalize and address in a systematic manner previous results in the subject.