The structure of the 3x + 1 problem
In: Electronic Journal of Graph Theory and Applications, Jg. 9 (2021), Heft 1, S. 157 - 174
2021Artikel/Aufsatz in ZeitschriftOA Gold
WirtschaftswissenschaftenMercator School of Management - Fakultät für Betriebswirtschaftslehre » Logistik und Operations Research
Damit verbunden: 1 Publikation(en)
Titel in Englisch:
The structure of the 3x + 1 problem
Autor*in:
Kimms, AlfUDE
- LSF ID
- 15707
- Sonstiges
- der Hochschule zugeordnete*r Autor*in
Erscheinungsjahr:
2021
Open Access?:
OA Gold
Web of Science ID
Scopus ID
Notiz:
OA platinum
Sprache des Textes:
Englisch
Erschienen in
Titel in Englisch (abgekürzt):
EJGTA
Verlag:
Institut Teknologi Bandung
in:
Jg. 9 (2021), Heft 1, S. 157 - 174
ISSN
ZDB ID
Ressourcentyp:
Text
Schlagwort, Thema:
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 Englisch:
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.