43741
2019
2019
eng
21
2nd version
report
1
2019-11-05
2019-11-05
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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.
10.25932/publishup-43741
urn:nbn:de:kobv:517-opus4-437416
Creative Commons - Namensnennung, 4.0 International
Eldar Sultanow
Christian Koch
Sean Cox
eng
uncontrolled
Collatz
eng
uncontrolled
Cayley Graph
eng
uncontrolled
Free Group
eng
uncontrolled
Reachability
Sozialwissenschaften
NUMBER THEORY
open_access
Wirtschaftswissenschaften
Second Version
Universität Potsdam
https://publishup.uni-potsdam.de/files/43741/collatz_sequences.pdf