Related papers: Collatz Problem of Positive Integers

The paper has been withdrawn by the author.

The paper was retracted.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.

This paper has been withdrawn by the author due to essential mistakes in some previous versions.

This paper has been withdrawn by the author because eq.(4) and those subsequent are incorrect.

This paper has been withdrawn by the author due to a crucial error in equation (51).

This paper has been withdrawn by the author due to a crucial error.

Major mistake. The paper has been withdrawn.

This paper has been withdrawn by the author due to an error in the derivation.

This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

This paper is wrong and is therefore withdrawn.

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This paper has been withdrawn by the author due to a crucial error in equation.

%auto-ignore This paper has been withdrawn by the author, due to a crucial error.

This paper has been withdrawn by the author for further investigation.

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.