Related papers: On Schurs exponent conjecture and its relation to …
We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, answers a question of Lampert on the…
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045]. Several…
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
New cases of the multiplicity conjecture are considered.
In this paper we investigate the recent advances by Zhang, Maynard and Pintz towards Polignac's conjecture and give some new results concerning the relationship between Polignac numbers and arithmetic progressions.
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
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…
The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and…
We present a new conjecture for the $SU_q(N)$ Perk-Schultz models. This conjecture extends a conjecture presented in our article (Alcaraz FC and Stroganov YuG (2002) J. Phys. A vol. 35 pg. 6767-6787, and also in cond-mat/0204074).
In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture,…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian…
This article presents a list of open questions on higher rank Brill-Noether theory and coherent systems. Background material and appropriate references are included.
We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.
Various origins of linear and nonlinear Schrodinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new…
The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…