Related papers: Proof of Union-Closed Sets Conjecture
The Frankl conjecture, also known as the union-closed sets conjecture, states that in any finite non-empty union-closed family, there exists an element in at least half of the sets. From an optimization point of view, one could instead…
We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
We provide a proof of the Borwein Conjecture using analytic methods.
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
We prove several extensions of the Erdos-Fuchs theorem.
We survey recent developments on the Restriction conjecture.
Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We prove a noncommutative version of Bishop's peak interpolation-set theorem.
In this note, we present a simpler way to prove the compactness of the closed intervals in simply ordered set with order topology.
In this paper we prove the WALA conjecture.
We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenomenon for Ulam sets U(a,b) as b increases. Based on this, we…
Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.
We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
We show the Graceful Tree Conjecture holds.
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.