On the stopping time of the Collatz map in $\mathbb{F}_2[x]$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917560372428800 |
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| author | Alon, Gil Behajaina, Angelot Paran, Elad |
| author_facet | Alon, Gil Behajaina, Angelot Paran, Elad |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_03210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stopping time of the Collatz map in $\mathbb{F}_2[x]$ Alon, Gil Behajaina, Angelot Paran, Elad Combinatorics Number Theory 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. |
| title | On the stopping time of the Collatz map in $\mathbb{F}_2[x]$ |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2401.03210 |