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 discipline

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

@article{909768b2b1d54260b62ee2cabf16b7f9,

title = "On the stopping time of the Collatz map in F2[x]",

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.",

keywords = "Collatz map, Finite fields, Polynomials",

author = "Gil Alon and Angelot Behajaina and Elad Paran",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = oct,

doi = "10.1016/j.ffa.2024.102473",

language = "אנגלית",

volume = "99",

journal = "Finite Fields and Their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - On the stopping time of the Collatz map in F2[x]

AU - Alon, Gil

AU - Behajaina, Angelot

AU - Paran, Elad

PY - 2024/10

Y1 - 2024/10

N2 - 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.

AB - 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.

KW - Collatz map

KW - Finite fields

KW - Polynomials

UR - http://www.scopus.com/inward/record.url?scp=85199960809&partnerID=8YFLogxK

U2 - 10.1016/j.ffa.2024.102473

DO - 10.1016/j.ffa.2024.102473

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85199960809

SN - 1071-5797

VL - 99

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

M1 - 102473

ER -