Related papers: A short proof of the irreflexivity conjecture
We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing…
In this work we tried to prove the lonely runner conjecture also known as the view obstruction problem.
In this paper we prove the WALA conjecture.
It is shown that the Poincar\'e-Birkhoff fixed point theorem may be proven by extending the geometric approach originally devised by Henri Poincar\'e himself, along with several results from elementary differential topology. Beginning with…
We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in Devroye and James "On simulation and properties of the stable…
We provide a shorter proof to Defant and Kravitz's theorem (arXiv:2201.03461, Theorem 1.2) on the length of Hitomezashi loops modulo 8.
This article gives a self-contained proof of Mostow Rigidity, at least modulo undergrad real analysis. The proof should be accessible to grad students interested in geometry and topology. It has no new research, but I think that this is an…
This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
In the paper it is demonstrated that Bells theorem is an unprovable theorem.
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.
This paper presents a rigidity property of the exceptional locus of some kind of small birational contractions. An application in the context of geometric transitions and Calabi-Yau threefolds moduli space is then given, with some physical…
This short note establishes an abstract Hales--Jewett theorem for semigroups equipped with a finite family of retractions. The proof relies on the interplay between retractions and tensor products of ultrafilters.
This is an addendum to a previous article, which aims to provide the proofs of some results in that paper (Theorem 7.5 and Proposition 9.15) which were removed from its final version. The reason for such omission is that these proofs follow…
We give a proof of some small weight and level cases of Serre's conjecture.
Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning.…
We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…