Related papers: Another simple proof of the 1-dimensional flat cha…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

We present a simple inductive proof of the Lagrange Inversion Formula.

We prove Simon's conjecture for 3-manifolds.

We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.

Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using…

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

We give an elementary proof to Hasse theorem.

We present a simpler proof of Naji's characterization of circle graphs.

In this paper, we present a short proof of Halin's grid theorem.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.

In this short paper we review and extract some features of the Fredholm Alternative problem .

These notes are a self-contained short proof of the stability of persistence diagrams.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.