相关论文: The Slope Polynomial and Collinear Points in Permu…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
The paper is withdrawn by the author due to an oversimplified and misleading approach which was taken initially as a starting point.
This paper was removed by arXiv admin due to 94% plagiarism from uncited reference hep-th/0507153.
The paper has been withdrawn by the author, due to a fatal error. A horse stumbles that has four legs.
This paper has been withdrawn by the author due to an error.
This paper has been withdrawn.
The paper has been withdrawn due to an error in the main theorem.
The paper is withdrawn because the analysis appeared to be incomplete.
In this paper we prove that among the permutations of length n with i fixed points and j excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for all given i,j<=n. We use a new technique involving diagonals of…
This paper has been withdrawn by the author due to an error.
This paper has been withdrawn by the author due to a crucial sign error in equation 1
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
We identify a surprising inequality satisfied by elementary symmetric polynomials under the action of the fixed point measure of a random permutation. Concretely, for any collection of $n$ non-negative real numbers $a_1, \dots, a_n \in…
This paper has been withdrawn by the author due to a crucial sign error in equation 1
The paper was retracted.
This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.
The stationary point of Problem 2 is NOT the stationary point of Problem 1. We are sorry and we are working on fixing this error.
This paper has been withdrawn.
This paper has been withdrawn by the author due to a crucial sign error in equation 1
For recursively generated shifts, we provide definitive answers to two outstanding problems in the theory of unilateral weighted shifts: the Subnormality Problem ({\bf SP}) (related to the Aluthge transform) and the Square Root Problem…