On the stopping time of the Collatz map in $\mathbb{F}_2[x]$
Combinatorics
2024-01-09 v1 Number Theory
Abstract
We study the stopping time of the Collatz map for a polynomial , and bound it by , improving upon the quadratic bound proven by Hicks, Mullen, Yucas and Zavislak. We also prove the existence arithmetic sequences of unbounded length in the stopping times of certain sequences of polynomials, a phenomenon observed in the classical Collatz map.
Cite
@article{arxiv.2401.03210,
title = {On the stopping time of the Collatz map in $\mathbb{F}_2[x]$},
author = {Gil Alon and Angelot Behajaina and Elad Paran},
journal= {arXiv preprint arXiv:2401.03210},
year = {2024}
}