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This paper has been withdrawn by the author due to a crucial sign error in equation.
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We study the counts of smooth permutations and smooth polynomials over finite fields. For both counts we prove an estimate with an error term that matches the error term found in the integer setting by de Bruijn more than 70 years ago. The…
This paper has been withdrawn by the author, due a crucial error in the proof of the main Theorem (Sec. 3). In particular, in deriving the bound on the probability of error (Eq. 10) the contribution of those pairs (x', y') that are not…
This paper has been withdrawn because the Editor of Electronical Journal of Statistics declined the paper.
This paper has been withdrawn by the author due to an error in the proof.
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This article is withdrawn because of a mistake in the main result of the paper.
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This paper has been withdrawn by the authors due to some errors.
This paper has been withdrawn by the author due to a mistake in one of the main lemmas.
In this paper, the asymptotic formulas for Eulerian numbers, refined Eulerian numbers and the coefficients of descent polynomials are obtained directly from the spline interpretations of these numbers. Having related these numbers directly…
This paper has been withdrawn by the author due to an error in the derivation.
This paper has been withdrawn by the author because it has been substantially modified.
This paper has been withdrawn by the author(s), due an error in the proof.
Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…
This paper has been withdrawn by the author due to an error in equations 39 and 41.
This paper has been withdrawn by the author because there are some typos in proofs.
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Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…