Counting points on Hessenberg Varieties over finite fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914112042172416 |
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| author | Abreu, Alex Nigro, Antonio Ram, Samrith |
| author_facet | Abreu, Alex Nigro, Antonio Ram, Samrith |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting points on Hessenberg Varieties over finite fields Abreu, Alex Nigro, Antonio Ram, Samrith Combinatorics Algebraic Geometry 11G25, 15B33, 05E05, 05E10 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. |
| title | Counting points on Hessenberg Varieties over finite fields |
| topic | Combinatorics Algebraic Geometry 11G25, 15B33, 05E05, 05E10 |
| url | https://arxiv.org/abs/2411.05096 |