On recurrence relations arising from NRS(2) applied to a cubic polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911444809809920 |
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| author | DeFranco, Mario |
| author_facet | DeFranco, Mario |
| contents | We prove that the leading coefficient of the "error" terms of NRS(2) applied to a cubic polynomial $f(z)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient rational functions in the zeros of $f(z)$. We express these terms as a sum over combinatorial objects which we call radius-value trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On recurrence relations arising from NRS(2) applied to a cubic polynomial DeFranco, Mario Combinatorics We prove that the leading coefficient of the "error" terms of NRS(2) applied to a cubic polynomial $f(z)$ with starting point $(-\frac{a_1}{a_2}, -\frac{a_1}{a_2})$ are positive-coefficient rational functions in the zeros of $f(z)$. We express these terms as a sum over combinatorial objects which we call radius-value trees. |
| title | On recurrence relations arising from NRS(2) applied to a cubic polynomial |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.12494 |