Counting points on Hessenberg Varieties over finite fields
Combinatorics
2025-10-27 v2 Algebraic Geometry
Abstract
We give a counting formula in terms of modified Hall-Littlewood polynomials and the chromatic quasisymmetric function for the number of points on an arbitrary Hessenberg variety over a finite field. As a consequence, we express the Poincar\'e polynomials of complex Hessenberg varieties in terms of a Hall scalar product involving the symmetric functions above. We use these results to give a new proof of a combinatorial formula for the modified Hall-Littlewood polynomials.
Cite
@article{arxiv.2411.05096,
title = {Counting points on Hessenberg Varieties over finite fields},
author = {Alex Abreu and Antonio Nigro and Samrith Ram},
journal= {arXiv preprint arXiv:2411.05096},
year = {2025}
}
Comments
16 pages, 3 figures