Related papers: The Eisenbud-Green-Harris Conjecture
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.
The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…
In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In…
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a…
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.
There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy…
We survey results related to the important Hossz\'u-Gluskin Theorem on $n$-ary groups adding also several new results and comments. The aim of this paper is to write all such results in uniform and compressive forms. Therefore some proofs…
In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite. In some cases, we are able to prove the conjectured recurrence. In some cases, we are not able to…
Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. Both instances of coinductive reasoning appeared in the literature before, but a…
This is a companion note to our paper 'Some advances on Sidorenko's conjecture', elaborating on a remark in that paper that the approach which proves Sidorenko's conjecture for strongly tree-decomposable graphs may be extended to a broader…
Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] established sharp Wilker and Huygens-type inequalities. These…
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
The paper is devoted to a somewhat idiosyncratic account of the theorem of de Bruijn-Erd\"{o}s and Hanani from the combinatorics of finite geometries and its various proofs. Among the proofs discussed are the original proofs by de…
In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.
In the paper, there are new found methods to determine the range of every exceptional element in exceptional set, we can solve Twin primes problem and Goldbach Conjecture problem basically.