Related papers: A simple proof of a conjecture on univariate polyn…
This paper has been withdrawn by the authors due to a crucial gap in the estimates for m>=4.
This paper has been withdrawn by the author.
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
This paper has been withdrawn by the authors
The article presents the proof of Casas-Alvero conjecture.
A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
The Poupard polynomials are polynomials in one variable with integer coefficients, with some close relationship to Bernoulli and tangent numbers. They also have a combinatorial interpretation. We prove that every Poupard polynomial has all…
This paper has been withdrawn because of serious errors.
This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2
This paper has been withdrawn by the author due to a crucial error in the Proof of Theorem 0.3
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
The combinatorial structure of a d-dimensional simple convex polytope can be reconstructed from its abstract graph [Blind & Mani 1987, Kalai 1988]. However, no polynomial/efficient algorithm is known for this task, although a polynomially…
The paper is withdrawn.
Recently the problem of constructing a perfect Euler cuboid was related with three conjectures asserting the irreducibility of some certain three polynomials depending on integer parameters. In this paper a partial result toward proving the…
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
An outstanding conjecture on roots of Ehrhart polynomials says that all roots $\alpha$ of the Ehrhart polynomial of an integral convex polytope of dimension $d$ satisfy $-d \leq \Re(\alpha) \leq d-1$. In this paper, we suggest some…
Withdrawn by the authors due to an error in the proof of the finite field result (Thm. 1.5): The random primes used in the proof need NOT avoid the exceptional primes from Lemma 2.7, thus leaving Thm. 1.5 unproved.
In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions. This implies a positive answer to Shapiro's conjecture for…