Related papers: A simple proof of a conjecture on univariate polyn…
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…
This paper is withdrawn.
This paper has been withdrawn.
This paper has been withdrawn.
We present an elementary proof of a conjecture proposed by I. Rasa in 2017 which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive by A. Komisarski and T. Rajba very recently by the use…
This paper has been withdrawn by the author due to a crucial error in eq.59. I apologize for the inconveniences.
This paper has been withdrawn by the authors, the main result being known since Lam and Leung, J. Algebra 2000.
This paper has been withdrawn by the author, due to possible counter-examples.
The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.
We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.
A recent conjecture by I. Ra\c{s}a asserts that the sum of the squared Bernstein basis polynomials is a convex function in $[0,1]$. This conjecture turns out to be equivalent to a certain upper pointwise estimate of the ratio…
Withdrawn because of non-correctness. Would have implied too much to be true :-|
We present counterexamples to a 30-year-old conjecture of Las Vergnas [J. Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.
This note gives a new elementary proof of Poincar\'e-Miranda theorem based on Sard's theorem and the simple classification of one-dimensional manifolds.
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
This paper has been withdrawn.
This paper has been withdrawn by the author due to a mistake in one of the main lemmas.
This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.
We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.
This paper has been withdrawn by the author.