Noncommutative Symmetric Functions and Lagrange Inversion II: Noncrossing partitions and the Farahat-Higman algebra

TL;DR

This paper develops new dual bases in noncommutative symmetric and quasi-symmetric functions, extending results on noncrossing partitions and deriving a quasi-symmetric version of the Farahat-Higman algebra.

Contribution

It introduces a novel pair of dual bases and generalizes key algebraic structures related to noncrossing partitions and the Farahat-Higman algebra.

Findings

Established new dual bases for noncommutative symmetric functions

Generalized results on the incidence algebra of noncrossing partitions

Derived a quasi-symmetric version of the Farahat-Higman algebra

Abstract

We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing partitions. As a consequence, we obtain a quasi-symmetric version of the Farahat-Higman algebra.