On the stopping time of the Collatz map in F2[x]

Gil Alon; Angelot Behajaina; Elad Paran

doi:10.1016/j.ffa.2024.102473

On the stopping time of the Collatz map in F₂[x]

Gil Alon
, Angelot Behajaina
, Elad Paran

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the stopping time of the Collatz map for a polynomial f∈F₂[x], and bound it by O(deg(f)^1.5), improving upon the quadratic bound proven by Hicks, Mullen, Yucas and Zavislak. We also prove the existence of arithmetic sequences of unbounded length in the stopping times of certain sequences of polynomials, a phenomenon observed in the classical Collatz map.

Original language	English
Article number	102473
Journal	Finite Fields and Their Applications
Volume	99
DOIs	https://doi.org/10.1016/j.ffa.2024.102473
State	Published - Oct 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Collatz map
Finite fields
Polynomials

Access to Document

10.1016/j.ffa.2024.102473

Cite this

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KW - Finite fields

KW - Polynomials

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