相关论文: The Slope Polynomial and Collinear Points in Permu…

The paper is withdrawn.

withdrawed due to a substantial error.

This paper has been withdrawn by the authors due to some fatal errors that cannot be mended. The authors apologize for any inconvenience.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.

This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

This paper has been withdrawn by the author due to a crucial error in Lemma 3.5.

This paper has been withdrawn by the author due to a crucial error.

Removed because of inappropriateness for e-print archives.

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.

This paper has been withdrawn by the author due to a mistake in the section 4.

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

This paper has been withdrawn

This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and…

This paper has been withdrawn by the author due to a crucial error in formula 4.12.r

This paper has been withdrawn by the author due to some error in the result

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.