Year: 2026
Type: preprint
Abstract: Let $λ, μ, ν$ be distinct partitions such that $λ, μ\subset ν$ and $|ν/λ|=|ν/μ|=1$. We prove Butler's positivity conjecture posed in 1994: the expansion of the Macdonald intersection polynomial \[ \frac{T_λ\widetilde{H}_μ(X;q,t)-T_μ\widetilde{H}_λ(X;q,t)}{T_λ-T_μ} \] in terms of the Schur function basis has coefficients in $\mathbb{Z}_{\geq 0}[q,t]$.
Source: arXiv (Cornell University)
Authors: Guo, Peter L., Kang, Mingyang, Xiong, Rui
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1288550874
OpenAlex ID: W7202350184
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