Analytic properties of Speyer's $g$-polynomial of uniform matroids
| Autor: | Zhang, Rong, Zhao, James Jing Yu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages |
| Databáze: | arXiv |
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