Related papers: On Schurs exponent conjecture and its relation to …

In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.

In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step…

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

In the preprint of 1993 the author formulated some conjectures on monotonicity of ratios for exponential series remainders. They are equivalent to conjectures on monotonicity of a ratio of Kummer hypergeometric functions and presumably not…

This paper aims to expand and detail the notion of formal semantics of Conjectures by applying a theoretic-model approach. After a short introduction to the concepts and basics of Conjectures, we will start from the notion of Simple…

This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schubert polynomials into key polynomials, and refines another one…

This paper presents a natural generalisation of Saxl conjecture from a Lie-theoretical perspective, which is verified for the exceptional types. For classical types, progress is made using spin representations, revealing connections to…

We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.

We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…

We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.

The Onsager's conjecture has two parts: conservation of energy, if the exponent is larger than $1/3$ and the possibility of dissipative Euler solutions, if the exponent is less or equal than $1/3$. The paper proves half of the conjecture,…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also…

A conjecture regarding the structure of expander graphs is discussed.

For any \theta<1/10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are H\"older-continuous with exponent \theta. A famous conjecture of Onsager states the existence of…

Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.

There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove…

This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by…