# Kazhdan-Lusztig R-polynomials for pircons

## TL;DR

This paper develops a unified combinatorial framework for various generalizations of Kazhdan-Lusztig R-polynomials, including parabolic, zircon, and Vogan polynomials, enhancing understanding of their interrelations.

## Contribution

It introduces a common combinatorial approach that encompasses multiple Kazhdan-Lusztig R-polynomial generalizations, facilitating broader analysis.

## Key findings

- Unified combinatorial framework established
- Connections between different R-polynomial variants clarified
- Potential for new applications in representation theory

## Abstract

The purpose of this work is to provide a common combinatorial framework for some of the analogues and generalizations of Kazhdan-Lusztig R-polynomials that have appeared since the introduction of these remarkable polynomials (e.g., parabolic Kazhdan-Lusztig R-polynomials, Kazhdan-Lusztig R-polynomials of zircons, and Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions).