Counting points on Hessenberg varieties over finite fields
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 Poincaré 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.
Authors
- Samrith Ram (ORCID: https://orcid.org/0000-0001-5870-3452)
- Antonio Nigro (ORCID: https://orcid.org/0000-0003-3466-7922)
- Alex Abreu (ORCID: https://orcid.org/0000-0002-8349-0097)
Institutions
- Indraprastha Institute of Information Technology Delhi (IN)
- Universidade Federal Fluminense (BR)
Publication Details
- Journal
- Algebraic Combinatorics
- Published
- 2026-10-27
- DOI
- https://doi.org/10.5802/alco.519
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Department of Science and Technology, Ministry of Science and Technology, India
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Russian Science Foundation