相关论文: On the Koszul Betti numbers in positive characteri…

This paper has been withdrawn by the authors due to an error in the main theorem.

This paper was withdrawn by the authors.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author due to an error in the last paragraph of step 2 of the main proof, on page 6.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

This paper has been withdrawn due to a crucial theoretical and experimental error.

We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

The paper has been withdrawn because the proof of part (b) of the main theorem is incomplete.

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

This paper has been withdrawn by the author, due an error in claim 1.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

The paper is withdrawn.

This paper has been withdrawn due to an error in the proof of the main theorem.

This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.

The paper has been withdrawn by the authors. The contents of the paper will be used in a future communication which will contain major addition and shift of focus.

This paper has been withdrawn by the author. Lemma 8 is used in the proof of Lemma 6, but it is not correct. Lemma 6 is essential for the main results.

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.