Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization

TL;DR

This paper introduces a method to construct dual bases for non-commutative symmetric and quasi-symmetric functions using Schützenberger's monoidal factorization, advancing the algebraic understanding of these functions.

Contribution

It provides a new effective construction of dual bases for non-commutative symmetric and quasi-symmetric functions leveraging monoidal factorization.

Findings

Constructed dual bases explicitly using monoidal factorization

Enhanced algebraic tools for non-commutative symmetric functions

Potential applications in combinatorics and algebraic structures

Abstract

In this work, an effective construction, via Sch\"utzenberger's monoidal factorization, of dual bases for the non commutative symmetric and quasi-symmetric functions is proposed.