Related papers: Simple Proofs of two Dirac-type Theorems Involving…

We provide a short proof of the 1-dimensional flat chain conjecture.

We present a short proof, relaying on the divergence theorem, verifying that minimal sets in the plane are trivial.

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…

The textbook proofs of Commoner's theorem characterizing liveness in free-choice Petri nets are given in contexts of technical notions and claims that make the proofs look a bit long. The aim of this note is to give a concise self-contained…

We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.

We refine a property of $2$-connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that each $2$-connected $n$-vertex graph with minimum degree at…

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

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

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

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

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We describe two distinct simple, short and self contained proofs of the composition lemma.

We provide simple proofs of analogues for coverings numbers of lattices of several recently studied basic statements on the ranks of tensors. We highlight the differences and analogies between the proofs in both settings.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

Under a slightly stronger hypothesis, one improves a connectedness result of Debarre [D] for a product of two projective spaces in terms of the extension problem of formal-rational functions (see Theorems 1.3 and 1.4 of the introduction)

We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition 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…

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.