Related papers: Another simple proof of the 1-dimensional flat cha…
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
We obtain new partial results supporting the spectral set conjecture in dimension 1.
We prove in this note a stabilized version of a conjecture on $\A^1$-connectedness. For the stabilized version of this conjecture, we introduce the notion of stable $\A^1$-connectedness, which is can be seen as the stabilization of…
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
We survey recent developments on the Restriction conjecture.
This note presents a simple proof of the monotonicity of the invariant distribution of a discrete Markov chain with a finite state space. This answers a question recently raised by David Siegmund.
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
Several results about the union-closed sets conjecture are presented.
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form…
We report a simple rigidity theorem for certain Euler products.
According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.
This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.
We generalize Pappus chain theorem and give an analogue to this theorem.
We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
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…