Related papers: On the Koszul Betti numbers in positive characteri…
This paper has been withdrawn for the reasons mentioned in the Comments.
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.
This paper is withdrawn by the authors, a better version is available as hep-ph/0505139.
This paper has been withdrawn by the author due to a crucial error in the last lines in the proof of Lemma 3.3.
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
This paper has been withdrawn by the authors, due to a flaw in the proof of Theorem 1. This preprint is superseded by quant-ph/0610027, where a correct proof can be found. Thanks to Rainer Siegmund-Schultze for spotting the error.
This work concerns commutative algebras of the form $R=Q/I$, where $Q$ is a standard graded polynomial ring and $I$ is a homogenous ideal in $Q$. It has been proposed that when $R$ is Koszul the $i$th Betti number of $R$ over $Q$ is at most…
The paper has been withdrawn.
In this survey paper, we present the broad outlines of the proof of a character formula for tilting representations of reductive algebraic groups in positive characteristic, obtained partly in collaboration with several other authors. A…
This paper has been withdrawn due to a error in Theorem 3.1.
This paper has being withdrawn by the authors due to an error in the conclusion.
We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…
This paper has been withdrawn by the authors due to need of essential revision.
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .
This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.
This paper has been withdrawn by author due to an error in the proof.
This paper has been withdrawn by the authors due to inadequate arguments.
This paper has been withdrawn. The main technical result will reappear in the new version of quant-ph/0501003.
In this paper a result of Latala about the tail behavior of Gaussian polynomials will be discussed. Latala proved an interesting result about this problem in paper [2]. But his proof applied an incorrect statement at a crucial point. Hence…