Analytic properties of Speyer's $g$-polynomial of uniform matroids
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914927082471424 |
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| author | Zhang, Rong Zhao, James Jing Yu |
| author_facet | Zhang, Rong Zhao, James Jing Yu |
| contents | Let $U_{n,d}$ denote the uniform matroid of rank $d$ on $n$ elements. We obtain some recurrence relations satisfied by Speyer's $g$-polynomials $g_{U_{n,d}}(t)$ of $U_{n,d}$. Based on these recurrence relations, we prove that the polynomial $g_{U_{n,d}}(t)$ has only real zeros for any $n-1\geq d\geq 1$. Furthermore, we show that the coefficient of $g_{U_{n,[n/2]}}(t)$ is asymptotically normal by local and central limit theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic properties of Speyer's $g$-polynomial of uniform matroids Zhang, Rong Zhao, James Jing Yu Combinatorics Primary 05B35, 26C10, Secondary 60F05, 62E20 Let $U_{n,d}$ denote the uniform matroid of rank $d$ on $n$ elements. We obtain some recurrence relations satisfied by Speyer's $g$-polynomials $g_{U_{n,d}}(t)$ of $U_{n,d}$. Based on these recurrence relations, we prove that the polynomial $g_{U_{n,d}}(t)$ has only real zeros for any $n-1\geq d\geq 1$. Furthermore, we show that the coefficient of $g_{U_{n,[n/2]}}(t)$ is asymptotically normal by local and central limit theorems. |
| title | Analytic properties of Speyer's $g$-polynomial of uniform matroids |
| topic | Combinatorics Primary 05B35, 26C10, Secondary 60F05, 62E20 |
| url | https://arxiv.org/abs/2408.15506 |