Postnikov--Stanley polynomials are Lorentzian
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909431281745920 |
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| author | An, Serena Tung, Katherine Zhang, Yuchong |
| author_facet | An, Serena Tung, Katherine Zhang, Yuchong |
| contents | Postnikov--Stanley polynomials $D_u^w$ are a generalization of skew dual Schubert polynomials to the setting of arbitrary Weyl groups. We prove that Postnikov--Stanley polynomials are Lorentzian by showing that they are degree polynomials of Richardson varieties. Our result yields an interesting class of Lorentzian polynomials related to the geometry of Richardson varieties, generalizes the result that dual Schubert polynomials are Lorentzian (Huh--Matherne--Mészáros--St. Dizier 2022), and resolves the conjecture that Postnikov--Stanley polynomials have M-convex support (An--Tung--Zhang 2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Postnikov--Stanley polynomials are Lorentzian An, Serena Tung, Katherine Zhang, Yuchong Combinatorics Algebraic Geometry Postnikov--Stanley polynomials $D_u^w$ are a generalization of skew dual Schubert polynomials to the setting of arbitrary Weyl groups. We prove that Postnikov--Stanley polynomials are Lorentzian by showing that they are degree polynomials of Richardson varieties. Our result yields an interesting class of Lorentzian polynomials related to the geometry of Richardson varieties, generalizes the result that dual Schubert polynomials are Lorentzian (Huh--Matherne--Mészáros--St. Dizier 2022), and resolves the conjecture that Postnikov--Stanley polynomials have M-convex support (An--Tung--Zhang 2024). |
| title | Postnikov--Stanley polynomials are Lorentzian |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2412.02051 |