A characterization of monotypically supersymmetric polynomials

TL;DR

This paper introduces a new algebraic object similar to supersymmetric polynomials, establishes its structure theorems, and explores its properties despite differences from classical supersymmetric polynomial theory.

Contribution

The paper develops the foundational structure theorems for a new algebraic object akin to supersymmetric polynomials, filling a gap in the theoretical understanding.

Findings

Established structure theorems for the new algebraic object

Demonstrated similarities and differences with classical supersymmetric polynomials

Provided foundational properties for future research

Abstract

We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new object, so we prove their counterpart for the new object.