Related papers: The Eisenbud-Green-Harris Conjecture

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

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…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We prove several extensions of the Erdos-Fuchs theorem.

The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…

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…

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.

We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.

We provide new sufficient conditions under which Ryser's conjecture holds.

We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…

This paper is a preliminary report on our search for new good examples of Hall's Conjecture. We present a new algorithm that will detect all good examples within a given search space. We have implemented the algorithm, and our executions…