Work

Macdonald intersections and the $N!/k$ conjecture

Year: 2026

Type: preprint

Abstract: We prove the Frobenius characteristic formula for the intersection of Garsia--Haiman modules predicted in the Science Fiction of Bergeron and Garsia. As a consequence, we resolve the $N!/k$ conjecture. The proof uses the geometry of the Hilbert scheme of points on the plane developed by Haiman.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2611.09638

Authors: Guo, Peter L., Kang, Mingyang, Su, Changjian, Xiong, Rui

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225632501

Cites: 4

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Related to: 10