Related papers: Yet another proof of Brooks' 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…

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

We provide a simple proof of Kamp's theorem.

An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.

A short and almost elementary proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem on the multiplicity of covering by simplices in $\mathbb R^d$ is given.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

A very simple but useful almost sure convergence theorem of probability is given.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…

The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.

We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.

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

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

We present in this work a new and simple proof of the false centre theorem.

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being…

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.

We prove several extensions of the Erdos-Fuchs theorem.

We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the…