Grove polynomials and $K$-theoretic quasisymmetry
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916037184716800 |
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| author | Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| author_facet | Nadeau, Philippe Spink, Hunter Tewari, Vasu |
| contents | We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are $K$-theoretically dual to the quasisymmetric Schubert cells which pave the quasisymmetric flag variety, in the same way that Grothendieck polynomials are dual to Schubert cells in the complete flag variety. As a consequence, the finite truncations of the multi-fundamental quasisymmetric functions of Lam-Pylyavskyy acquire a geometric interpretation as $K$-theoretic representatives of quasisymmetric Schubert cells. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22750 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grove polynomials and $K$-theoretic quasisymmetry Nadeau, Philippe Spink, Hunter Tewari, Vasu Combinatorics We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are $K$-theoretically dual to the quasisymmetric Schubert cells which pave the quasisymmetric flag variety, in the same way that Grothendieck polynomials are dual to Schubert cells in the complete flag variety. As a consequence, the finite truncations of the multi-fundamental quasisymmetric functions of Lam-Pylyavskyy acquire a geometric interpretation as $K$-theoretic representatives of quasisymmetric Schubert cells. |
| title | Grove polynomials and $K$-theoretic quasisymmetry |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.22750 |