The structure of the 3x + 1 problem
In: Electronic Journal of Graph Theory and Applications, Vol. 9 (2021), No. 1, pp. 157 - 174
2021article/chapter in journalOA Gold
EconomicsMercator School of Management - Faculty of Business Administration » Logistics and Operations Research
Related: 1 publication(s)
Title in English:
The structure of the 3x + 1 problem
Author:
Kimms, AlfUDE
- LSF ID
- 15707
- Other
- connected with university
Year of publication:
2021
Open Access?:
OA Gold
Web of Science ID
Scopus ID
Note:
OA platinum
Language of text:
English
Title in English (abbreviated):
EJGTA
Publisher:
Institut Teknologi Bandung
in:
Vol. 9 (2021), No. 1, pp. 157 - 174
ISSN
ZDB ID
Type of resource:
Text
Keyword, Topic:
3x + 1 problem ; Collatz graph ; Collatz problem ; graph transformation ; Haase's algorithm ; hailstone numbers Mathematics ; Kakutani's problem ; Syracuse problem ; Thwaites' problem ; Ulam's problem
Abstract in English:
Paul Erdos said about the 3x + 1 problem, “Mathematics is not yet ready for such problems”. And he is seemingly right. Although we cannot solve this problem either, we provide some results about its structure. The so-called Collatz graph is iteratively transformed into a sequence of graphs by making use of some hidden structure information. It turns out that the transformation of graphs corresponds to a sequence of sets of numbers. It is shown that if the union of these number sets were equal to the set of integers greater than one, the famous Collatz conjecture would be true.