On composition polynomials

TL;DR

This paper offers a combinatorial interpretation of reduced composition polynomials and connects them to the $(1-q)$-transform of noncommutative symmetric functions, enriching the understanding of their algebraic structure.

Contribution

It introduces a new combinatorial perspective on composition polynomials and links them to noncommutative symmetric functions, advancing theoretical understanding.

Findings

Provides a combinatorial interpretation of reduced composition polynomials

Establishes a relationship with the $(1-q)$-transform of noncommutative symmetric functions

Enhances the algebraic understanding of composition polynomials

Abstract

We provide a combinatorial interpretation of the reduced composition polynomials of Ardila and Doker [Adv. Appl. Math. 50 (2013), 607], and relate them to the $(1-q)$-transform of noncommutative symmetric functions.