# Asymmetric function theory

## TL;DR

This paper surveys recent advancements in extending the classical symmetric function theory to encompass asymmetric polynomials, highlighting new algebraic structures and potential applications in combinatorics and related fields.

## Contribution

It introduces a comprehensive overview of how symmetric function theory has been generalized to asymmetric polynomials, expanding its scope and applicability.

## Key findings

- Extension of symmetric functions to asymmetric polynomials
- Connections to algebraic combinatorics and representation theory
- Potential new applications in enumerative geometry

## Abstract

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.

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Source: https://tomesphere.com/paper/1904.01358