Related papers: A Simple Proof of Sharkovsky's Theorem
The classic Mckay correspondence gives a connection between finite subgroups of $\operatorname{SU}(2)$ and the simply-laced Dynkin diagrams. In this article, a direct proof is presented. The bipartite structure of the Mckay diagrams is…
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
In this paper we show an index theorem for gerbes
We give a simplified proof of analyticity of pluripolar multifunctions
We prove the orderability of the Witzel-Zaremsky-Thompson group for a direct system of orderable groups under a certain compatibility assumption.
We give a concise exposition of Voevodsky's theory of motives.
We prove Shokurov's index conjecture for quotient singularities.
We prove that the automorphism group of the semigeneric directed graph (in the sense of Cherlin's classification) is uniquely ergodic.
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct…
In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…
This is a companion note to our paper 'Some advances on Sidorenko's conjecture', elaborating on a remark in that paper that the approach which proves Sidorenko's conjecture for strongly tree-decomposable graphs may be extended to a broader…
In this paper, we give a necessary condition for a diagram to represent the trivial knot.