Related papers: "A combinatorial universal $\star$-product" is inc…

The paper is withdrawn. The proof has an error and it requires a different approach.

The paper was withdrawn because of its significant overlap with a paper appeared recently.

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .

This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author due to a crucial error in the submission action.

This paper has been withdrawn by the authors due to a crucial error.

We identify and correct an erroneous formula for Euler numbers that appears in Hansen's Table of Series and Products. We also provide details about the history of this error.

In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…

Paper withdrawn. Error lemma 7.

This paper has been withdrawn by the author due to an error.

Some mistaken reasonings at the end of the paper omitted.

In this paper, we discuss a similar functional to that of a standard integral. The main difference is in its definition: instead of taking a sum, we are taking a product. It turns out this new "star-integral" may be written in terms of the…

This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.

A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…

A small error was corrected.

This paper has been withdrawn by the author due to the presented idea is wrong.

The paper presents a counterexample to the Hodge conjecture.

This paper has been withdrawn by the author, due to a crucial error in page 5.

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.