3 papers
math.CO2026
Combinatorial formulas for Macdonald polynomials by superizations
Emma Yu Jin, Xiaowei Lin
In this paper, we derive new combinatorial formulas for symmetric Macdonald polynomials and non-symmetric Macdonald polynomials , in terms of several new s…
math.CO2025
The monomial expansions of modified Macdonald polynomials
Emma Yu Jin, Xiaowei Lin
We discover a family of sixteen statistics on fillings of any given Young diagram and prove new combinatorial formulas for modified Macdonald polynomials, that is, $$\tilde{H}_…
math.CO2024
Modified Macdonald polynomials and mu-Mahonian statistics
Emma Yu Jin, Xiaowei Lin
The Haglund--Haiman--Loehr theorem provides the following combinatorial formula for the modified Macdonald polynomials: $$\tilde{H}_μ(X;q,t)=\sum_{σ: μ\rightarrow \mathbb{P}}x^σt^{…