# A major-index preserving map on fillings

## TL;DR

This paper introduces a generalized major-index preserving map on fillings that connects combinatorial models for key and Macdonald polynomials, leading to new insights and solutions in algebraic combinatorics.

## Contribution

It generalizes Mason's map to account for the major index and extends similar maps to models for modified Macdonald polynomials, addressing open questions.

## Key findings

- Established a major-index preserving map for key polynomial models.
- Extended the map to models for modified Macdonald polynomials at t=0.
- Provided a combinatorial framework that solves conjectures and questions in algebraic combinatorics.

## Abstract

We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. We also define similar variants of this map, that regards alternative models for the modified Macdonald polynomials at $t=0$, thus partially answer a question by J. Haglund. These maps imply certain uniqueness property regarding inversion-- and coinversion-free fillings, which allows us to generalize the notion of charge to a non-symmetric setting, thus answering a question by A. Lascoux. The analogous question in the symmetric setting proves a conjecture by K. Nelson.