Related papers: A Counting Proof of the Graham Pollak Theorem
A simple proof of Egorov's theorem for infinite measure is given
We give a direct proof of the Cotlar-Stein lemma, which does not rely on the power trick.
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
We prove a version of van der Corput's Lemma for polynomials over the p-adic numbers.
We prove an improved form of an expectation of Polya and discuss several related questions
Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.
In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.
A proof of the main theorem of the Galois theory is presented using the main theorem of symmetric polynomials. The idea originated from studying the "M\'emoire sur les conditions de r\'esolubilit\'e des \'equations par radicaux" of Evariste…
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We prove some new results related to Tanaka's formula.
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
We present an algebro-geometric proof of the K-semistability of the projective plane.