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This paper has been withdrawn by the author due to a crucial problem in Lemma 3.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This paper has been withdrawn. The results are now part of math.GR/9804072.
Large language models are increasingly used for many applications. To prevent illicit use, it is desirable to be able to detect AI-generated text. Training and evaluation of such detectors critically depend on suitable benchmark datasets.…
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This paper has been withdrawn by the authors due to the violation of ATLAS experiment publication policy.
This paper has been withdrawn.
The author was informed that the result in the original version had been obtained earlier by K. Ueda (arXiv:math/0503355 [math.AG]). The paper is retracted.
This paper has been withdrawn at the author's request.
Conducting literature reviews for scientific papers is essential for understanding research, its limitations, and building on existing work. It is a tedious task which makes an automatic literature review generator appealing. Unfortunately,…
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
In the present-day scenario, Large Language Models (LLMs) are establishing their presence as powerful instruments permeating various sectors of society. While their utility offers valuable support to individuals, there are multiple concerns…
This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.
This paper was withdrawn by the author due to an edition's rights
In light of recent legal allegations brought by publishers, newspapers, and other creators of copyrighted corpora against large language model developers who use their copyrighted materials for training or fine-tuning purposes, we propose a…
This submission has been withdrawn at the request of the author.
This paper has been withdrawn by the author due to a crucial sign error in equation 1
This paper has been withdrawn by the author: it was a too preliminary version.
This paper has been withdrawn due to its publication
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
This paper has been withdrawn by the author.