Analogues of the 3x+ 1 Problem in Polynomial Rings of Characteristic 2

DOI10.1080/10586458.2016.1227734zbMath1446.11045arXiv1610.02545OpenAlexW2529321690MaRDI QIDQ5374133

Daniel Nichols

Publication date: 9 April 2018

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02545

zbMATH Keywords

random walkdiscrete dynamical systemCollatz conjecture\(3x+1\)

Mathematics Subject Classification ID

Recurrences (11B37) Stopping times; optimal stopping problems; gambling theory (60G40) Special sequences and polynomials (11B83) Radix representation; digital problems (11A63) Factorization (11Y05)

Related Items (2)

The Collatz problem in \(\mathbb{F}_p [x\) and \(\mathbb{F}_p x\)] ⋮ A topological approach to the Ulam-Kakutani-Collatz conjecture

Cites Work

• Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)
• A generalization of the Syracuse algorithm in \({\mathbb{F}}_ q[x\)]
• Stochastic Models for the 3x+1 and 5x+1 Problems
• The Doctrine of Chances
• The 3x + 1 Problem and Its Generalizations
• An improved Monte Carlo factorization algorithm
• A stopping time problem on the positive integers
• A Polynomial Analogue of the 3n + 1 Problem

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