Related papers: The Slope Polynomial and Collinear Points in Permu…

This paper has been withdrawn by the author due to serious error found in main argument.

The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones…

This paper has been withdrawn by the authors due to a crucial gap in the estimates for m>=4.

Withdrawn due to critical error.

This paper is painfully withdrawn.

This paper is withdrawn due to some gaps in the proof

The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.

This paper has been withdrawn.

Paper withdrawn - lemma 4.1 was false. Quite a lot of changes need to be made!

This article has been withdrawn.

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

Let $\alpha:\mathbb{Z}_n\to\mathbb{Z}_n$ be a permutation and $\Psi(\alpha)$ be the number of collinear triples modulo $n$ in the graph of $\alpha$. Cooper and Solymosi had given by induction the bound…

This paper has been withdrawn due to a sign error in the equation for F_11 which invalidates many results.

This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.

This paper has been withdrawn by the author due to a crucial error in example.

This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.

Withdrawn by the authors due to an error in the proof of the finite field result (Thm. 1.5): The random primes used in the proof need NOT avoid the exceptional primes from Lemma 2.7, thus leaving Thm. 1.5 unproved.

The paper has been withdrawn due to numerical error.

This paper has been withdrawn by the author, due to a crucial error in page 5.

This paper has been withdrawn.