Related papers: Combinatorial shifting and graded Betti numbers

This paper has been withdrawn. It was an early draft submitted prematurely in error. A complete version is to be submitted shortly.

This paper has been withdrawn by the author due to a crucial error.

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This paper has been superseded by math.AG/0510287 and withdrawn by the author.

This paper has been withdrawn by the author due to the incorrect argument for the security.

This paper has been withdrawn. A much-improved version can be found at hep-ph/0209176.

This paper has been withdrawn by the author due to an error in the derivation.

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This paper has been withdrawn by the author due to similarity to Author's other paper

This paper was withdrawn and incorporated into section II of cond-mat/0310512

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

This paper has been withdrawn. The results are now part of math.GR/9804072.

This paper has been withdrawn by the authors, and instead we have replaced hep-ph/9807214 by this new version.

The paper has been withdrawn by authors. The issues studied in this paper were changed so much that we have published a new paper considering these issues. See hep-th/0406074

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The paper is being withdrawn. A new submission will follow.

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

This paper has been withdrawn by the authors because it has been merged with paper arXiv:0903.3501v1 [math.DG]

This paper has been withdrawn by the authour.

This paper has been withdrawn by the author.