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

A consequence of Ore's classic theorem characterizing the maximal graphs with given order and diameter is a determination of the largest such graphs. We give a very short and simple proof of this smaller result, based on a well-known…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

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

The note provides a simple proof of Kisin's theorem about the restriction of crystalline representations to certain subgroup of the Galois group.

We give a new independent proof of a generalised version of the theorem by Rashevskii, which appeared in [Uch. Zapiski Ped. Inst. K. 2 (1938), 83 -- 94] and from which the classical Chow-Rashevskii Theorem follows as a corollary. The proof…

Here is present short proofing of Jordan's theorem about dividing of flat on two disjoint subsets by one closed curve.

We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.

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

We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.

We prove a homotopy theorem for sheaves. Its application shortens and simplifies the proof of many Oka principles such as Gromov's Oka principle for elliptic submersions.

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.

Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…

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

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…

We give a counting based proof of the Graham Pollak Theorem

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.