Related papers: Proof of Union-Closed Sets Conjecture
The union-closed sets conjecture, also known as Frankl's conjecture, is a well-studied problem with various formulations. In terms of lattices, the conjecture states that every finite lattice $L$ with more than one element contains a…
We prove a combination theorem for PD(n)-pairs.
We prove inversion of adjunction on log canonicity.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We provide a short proof of the 1-dimensional flat chain conjecture.
In this paper the circulant Hadamard conjecture is proved.
The Frankl or Union-Closed Sets conjecture states that for any finite union-closed family of sets $\mathcal{F}$ containing some nonempty set, there is some element $i$ in the ground set $U(\mathcal F) := \bigcup_{S \in \mathcal{F}} S$ of…
We prove that the $abc$-Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use the $abc$-Conjecture to prove that there exist uniform bounds…
We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.
We prove inversion of adjunction for higher rational singularities.
We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on…
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
We prove Dejean's conjecture. Specifically, we show that Dejean's conjecture holds for the last remaining open values of n, namely 15 <= n <= 26.
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
A finite family $\mathrsfs{F}$ of subsets of a finite set $X$ is union-closed whenever $f,g\in\mathrsfs{F}$ implies $f\cup g\in\mathrsfs{F}$. These families are well known because of Frankl's conjecture. In this paper we developed further…
We obtain new partial results supporting the spectral set conjecture in dimension 1.