Related papers: Short proof of the Gallai-Edmonds Structure Theore…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

In this paper we present short algebraic proofs of the Linear Conway--Gordon--Sachs and the Linear van Kampen--Flores theorems in the spirit of the Radon theorem on convex hulls. {\bf Theorem.} {\it Take any $n+3$ general position points in…

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

We give a short proof of Ahlfors' theorem on covering surfaces.

We expose here a short proof of Cramer's theorem in R based on convex duality.

In this paper, we establish the theory of $\sigma$-solvable hypergroups, study some properties of $\sigma$-solvable hypergroups and give similar results of Hall's Theorem in $\sigma$-solvable hypergroups.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

Combining P\'{o}sa's rotation lemma with a technique of Kopylov in a novel approach, we prove a generalization of the Erd\H{o}s-Gallai theorems on cycles and paths. This implies a clique version of the Erd\H{o}s-Gallai stability theorems…

We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.

We will explain how elementary concepts of relative homological algebra yield the Taylor tower for functors from pointed categories to abelian groups recovering the constructions of Johnson and McCarthy.

We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.

We give a constructive proof of the Carath\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus.

We study the group of ends of a pro-p group G and prove a pro-p analog of Stallings' decomposition theorem.

We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

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

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

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 injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…

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.

A very short proof of Kneser's theorem via transversal is given.