Search results
Results from the WOW.Com Content Network
The first 21 levels of the Collatz graph generated in bottom-up fashion. The graph includes all numbers with an orbit length of 21 or less. There is another approach to prove the conjecture, which considers the bottom-up method of growing the so-called Collatz graph.
2010-03-07 16:29 TerrorBite 1440×1406× (532396 bytes) This is a graph, generated in bottom-up fashion, of the orbits of all numbers under the Collatz map with an orbit length of 20 or less.
graph theory: John Horton Conway: 150 Deligne conjecture: monodromy: Pierre Deligne: 788 Dittert conjecture: combinatorics: Eric Dittert: 11 Eilenberg−Ganea conjecture: algebraic topology: Samuel Eilenberg and Tudor Ganea: 96 Elliott–Halberstam conjecture: number theory: Peter D. T. A. Elliott and Heini Halberstam: 300 Erdős–Faber ...
Directed graph showing the orbits of the first 1000 numbers in the Collatz conjecture. The integers from 1 to 1000 are colored from red to violet according to their value. French
Lothar Collatz (German:; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia. The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.
Directed graph showing the orbits of the numbers less than 30 (with the exception of 27 because it would make it too tall) under the Collatz map. For a larger graph containing only odd numbers, see Image:Collatz-graph-300.svg. Created with Graphviz, with the help of this Python program:
The 3x + 1 semigroup has been used to prove a weaker form of the Collatz conjecture. In fact, it was in such context the concept of the 3 x + 1 semigroup was introduced by H. Farkas in 2005. [ 2 ] Various generalizations of the 3 x + 1 semigroup have been constructed and their properties have been investigated.
English: Directed graph showing the orbits of the odd numbers less than 50 (with the exceptions of 27, 31, 41, and 47, because they would make it too tall) under the Collatz map. For a larger graph, see :Image:Collatz-graph-300.svg .