PreprintCC BY 4.0arXiv
The e-expansion of integral form Macdonald polynomials
Abstract
In this paper, we investigate the expansion of the integral form Macdonald polynomials Jμ(x;q,t) in the elementary symmetric function basis. Motivated by the connection between chromatic symmetric functions and LLT polynomials, we conjecture the e-positivity of a normalization of Jμ(x;q,t). We verify the conjecture when μ is either a hook or a two-column partition. In the hook case, we express the e-coefficients as weighted sums over compositions. In the two-column case, we derive explicit formulas for the e-coefficients.
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BibTeX
@misc{haglund2026eexpansion,
title = {{The $e$-expansion of integral form Macdonald polynomials}},
author = {Jim Haglund and Jang Soo Kim and Jaeseong Oh and Meesue Yoo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34772},
eprint = {2610.34772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34772},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The e-expansion of integral form Macdonald polynomials
AU - Jim Haglund
AU - Jang Soo Kim
AU - Jaeseong Oh
AU - Meesue Yoo
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34772
UR - https://arxiv.org/abs/2610.34772
AB - In this paper, we investigate the expansion of the integral form Macdonald polynomials J_μ(x;q,t) in the elementary symmetric function basis. Motivated by the connection between chromatic symmetric functions and LLT polynomials, we conjecture the e-positivity of a normalization of J_μ(x;q,t). We verify the conjecture when μ is either a hook or a two-column partition. In the hook case, we express the e-coefficients as weighted sums over compositions. In the two-column case, we derive explicit formulas for the e-coefficients.
ER -