Word symmetric functions and the Redfield-P\'olya

TL;DR

This paper develops noncommutative analogues of the Redfield-Pólya theorem within the algebra of word symmetric functions and related combinatorial Hopf algebras, expanding the theoretical framework of symmetry enumeration.

Contribution

It introduces noncommutative versions of the Redfield-Pólya theorem in the context of word symmetric functions and related Hopf algebras, providing new algebraic tools for symmetry analysis.

Findings

Noncommutative Redfield-Pólya theorems established

Extension to various combinatorial Hopf algebras achieved

New algebraic structures for symmetry enumeration developed

Abstract

We give noncommutative versions of the Redfield-P\'olya theorem in WSym, the algebra of word symmetric functions, and in other related combinatorial Hopf algebras.