Related papers: Note: a counterexample to a conjecture of Gilmer w…

The paper presents a counterexample to the Hodge conjecture.

We provide a proof of the union-closed sets conjecture, by means of a suitable refinement of the breakthrough entropy-approach introduced by Gilmer. The novelty here is to consider a convex combination of $A$ and $A\cup B$, where $A,B$ are…

Several results about the union-closed sets conjecture are presented.

We prove Union-Closed sets conjecture.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

In this short note we present a family of counterexamples to the King's 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.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

In this paper, we give a simple counter example to the famous Hodge conjecture.

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

New cases of the multiplicity conjecture are considered.

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.

The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.

In a recent breakthrough, Gilmer proved the union closed conjecture up to a constant factor. Using Gilmer's method and additional ideas, Chase and Lovett proved an optimal result for almost union-closed set systems. Here that result is…

Mathematicians had little idea whether the easy-to-state union-closed conjecture was true or false even after $40$ years. However, last winter saw a surge of interest in the conjecture and its variants, initiated by the contribution of a…

In this short note we give counterexamples to several results related to extension theorems published recently.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

We survey the state of the union-closed sets conjecture.

A set system is called union closed if for any two sets in the set system their union is also in the set system. Gilmer recently proved that in any union closed set system some element belongs to at least a $0.01$ fraction of sets, and…