Related papers: Casas-Alvero Conjecture is true
We show that Wahl's conjecture holds in all characteristics for a minuscule G/P.
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We prove several extensions of the Erdos-Fuchs theorem.
Based on the recent work of Arsovski, we confirm a conjecture of Feng, Sun, and Xiang, and we give a shortened proof of Snevily's conjecture.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times…
We prove some new results related to Tanaka's formula.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
We prove the positivity conjecture for all skew-symmetric cluster algebras.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We show that conjecture 15 in the article by Rabern et al. is wrong, comment on theorem 24 there, and conclude with some remarks on structures similar to the Yablo construction.
We prove Simon's conjecture for 3-manifolds.
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.
In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…