相关论文: A Simple Proof of Sharkovsky's Theorem

In this note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due to Sudakov, Szemeredi and Vu, though the conclusion of our…

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

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.

Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.

A one-line proof of a minimax theorem due to Steinerberger is given.

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

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

The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on $n$ vertices by Kazakov--Korablev as a congruence modulo $2$, and its integral lift was given by…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…

A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…

By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

A simple proof of Egorov's theorem for infinite measure is given

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

We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.