On the stopping time of the Collatz map in $\mathbb{F}_2[x]$

Angelot Behajaina; Elad Paran; Gil Alon

arxiv: 2401.03210 · v1 · pith:PVW3A3ZR · submitted 2024-01-06 · math.CO · math.NT

On the stopping time of the Collatz map in mathbb{F}₂[x]

Gil Alon , Angelot Behajaina , Elad Paran This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel pith:PVW3A3ZR record.json open to challenge →

classification math.CO math.NT

keywords collatzstoppingboundmathbbsequencestimearithmeticcertain

0 comments

read the original abstract

We study the stopping time of the Collatz map for a polynomial $f \in \mathbb{F}_2[x]$, and bound it by $O({\rm deg} (f)^{1.5})$, 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.

This paper has not been read by Pith yet.

On the stopping time of the Collatz map in mathbb{F}₂[x]

discussion (0)