Related papers: A simple proof of a conjecture on univariate polyn…
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…
This article has been withdrown by the author.
This paper has been withdrawn by the author due to its main result being included in cond-mat/0403309 by the same author.
This paper has been withdrawn
In the paper I considered algebra of polynomials over associative D-algebra with unit. Using the tensor notation allows to simplify the representation of polynomial. I considered questions related to divisibility of polynomial of any power…
We prove that a random bivariate polynomial with plus minus 1 coefficients is irreducible with high probability.
In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an upper estimate for the Koebe radius of univalent…
This paper has been withdrawn by the author due to an error.
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals. We then deduce that for some classes of classical univariate orthogonal polynomials the Image Conjecture is…
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
This paper has been withdrawn by the author due a crucial error.
This paper has been withdrawn by the authors due to a mistake in the proof of the chief result. In particular Theorem 1.3 is correct, while Theorem 1.1 and Theorem 1.2 hold with \mu>0 and a suitable restriction on the exponent p. The proof…
In this paper we prove two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873], using a method for proving inequalities of mixed trigonometric polynomial functions.
This paper has been withdrawn by the author for further modification.
This paper has been withdrawn by the author becouse the conjecture presented in this paper is false. The correct study of metrics in interpolation spaces for and applcation to nonharmonic Fourier series will be published in S.Petersburg…
This paper was withdrawn by the author due to an edition's rights
This paper has been withdrawn by the author due a few mistakes in the paper.
This paper has been withdrawn by the author due to an error.
This paper has been withdrawn by the author due to an error
In this article, we verify the additivity for rank of a sum of coprime monomials and bivariate polynomials generalizing the result in (\cite{CCG}). We also show similar results hold for cactus rank.