A classification of bisymmetric polynomial functions over integral domains of characteristic zero

TL;DR

This paper characterizes the class of polynomial functions that satisfy bisymmetry over integral domains of characteristic zero, providing a comprehensive classification of such functions.

Contribution

It offers a complete classification of bisymmetric polynomial functions over integral domains of characteristic zero, extending previous results to a broader algebraic setting.

Findings

Identifies all bisymmetric polynomial functions over the specified domains.

Provides a structural description of these functions.

Extends known classifications to new algebraic contexts.

Abstract

We describe the class of n-variable polynomial functions that satisfy Acz\'el's bisymmetry property over an arbitrary integral domain of characteristic zero with identity.