English

On recurrence relations arising from NRS(2) applied to a cubic polynomial

Combinatorics 2026-02-16 v1

Abstract

We prove that the leading coefficient of the "error" terms of NRS(2) applied to a cubic polynomial f(z)f(z) with starting point (a1a2,a1a2)(-\frac{a_1}{a_2}, -\frac{a_1}{a_2}) are positive-coefficient rational functions in the zeros of f(z)f(z). We express these terms as a sum over combinatorial objects which we call radius-value trees.

Keywords

Cite

@article{arxiv.2602.12494,
  title  = {On recurrence relations arising from NRS(2) applied to a cubic polynomial},
  author = {Mario DeFranco},
  journal= {arXiv preprint arXiv:2602.12494},
  year   = {2026}
}
R2 v1 2026-07-01T10:34:37.819Z