Related papers: More simple proofs of Sharkovsky's theorem
We give a modern account of Agafonov's original proof of his eponymous theorem. The original proof was only reported in Russian in a journal not widely available, and the work most commonly cited in western literature is instead the English…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
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…
We obtain some results related to Romanoff's theorem.
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.
We present an alternative proof of Sanov's theorem for Polish spaces in the weak topology that follows via discretization arguments. We combine the simpler version of Sanov's Theorem for discrete finite spaces and well chosen finite…
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…
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
Sidorenko's conjecture states that the number of copies of any given bipartite graph in another graph of given density is asymptotically minimized by a random graph. The forcing conjecture further strengthens this, claiming that any…
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 present a simpler proof of Naji's characterization of circle graphs.
Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
A one-line proof of a minimax theorem due to Steinerberger is given.
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
Circular proofs, introduced by Daniyar Shamkanov, are proofs in which assumptions are allowed that are not axioms but do appear at least twice along a branch. Shamkanov has shown that a formula belongs to the provability logic GL exactly if…
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We give a simple inductive proof of this theorem.
The paper contains an alternative proof of M. Kontsevich Formality 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…
In this paper we present new proofs of the Conway-Gordon-Sachs and Sachs Theorems on the linked cycles in graphs embedded in $\R^3$. We reduce these theorems to certain property of graphs mapped to the plane.