A generalization of complete and elementary symmetric functions

TL;DR

This paper introduces a new generalization of classical symmetric functions, extending their generating functions and relationships, with combinatorial interpretations provided for the generalized functions.

Contribution

It presents a novel generalization of complete and elementary symmetric functions, expanding their theoretical framework and offering new combinatorial insights.

Findings

Generalized symmetric functions with new generating functions

Reformulation of classical relationships in a broader context

Combinatorial interpretations of the generalized functions

Abstract

In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and elementary symmetric functions are reformulated in a more general context. Combinatorial interpretations of these generalized symmetric functions are also introduced.