Related papers: Yet another proof of Brooks' theorem
We give a probabilistic proof of the orbit-counting lemma.
We provide a simple proof of Pascal's Theorem on cyclic hexagons, as well as a generalization by M\"obius, using hyperbolic geometry.
We provide a short proof of the 1-dimensional flat chain conjecture.
Here is present short proofing of Jordan's theorem about dividing of flat on two disjoint subsets by one closed curve.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We give a counting based proof of the Graham Pollak Theorem
This is an expository paper, giving a simplified proof of the cubic case of the main conjecture for Vinogradov's mean value theorem.
It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…
We settle in the affirmative the Graham-Sloane conjecture.
In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments…
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…
A type analysable in one-based types in a simple theory is itself one-based.
We prove a variation of Gronwall's lemma.
The non-transitivity without extra constraints in the Euler equation in any dimension is almost evident and can be derived, e.g., from Morse theory.
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of of irreducible curve singularities obtained by V.I.Arnold. The proof is essentially based on the method of…
This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.
We prove the Aharoni Berger Conjecture