Collatz Sequences in the Light of Graph Theory

  • The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequence’s "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means. The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.

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Author details:Eldar SultanowORCiDGND, Christian Koch, Sean Cox
Publication type:Report
Date of first publication:2019/11/05
Completion year:2019
Publishing institution:Universität Potsdam
Release date:2019/11/05
Tag:Cayley Graph; Collatz; Free Group; Reachability
Print run:2nd version
Page number:21
Organizational units:Wirtschafts- und Sozialwissenschaftliche Fakultät / Wirtschaftswissenschaften
DDC classification:3 Sozialwissenschaften / 30 Sozialwissenschaften, Soziologie / 300 Sozialwissenschaften
MSC classification:11-XX NUMBER THEORY
Collection(s):Universität Potsdam / Sondersammlungen / Collatz Sequences in the Light of Graph Theory / Second Version
License (German):License LogoCreative Commons - Namensnennung, 4.0 International