Related papers: A Counting Proof of the Graham Pollak Theorem
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.
We prove a combination theorem for PD(n)-pairs.
Polya Enumeration Theorem is one of the most useful tools dealing with the enumeration of patterns that are symmetric in some ways. What follows is a procedure for obtaining the results of Polya Theorem directly, bypassing the usual…
A proof of Sendov's conjecture is given.
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.
We prove a local version of the Mazur-Ulam theorem.
There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…
In this note we give a detailed proof of a theorem of Aubin.
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
We prove several extensions of the Erdos-Fuchs theorem.
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
We present a simple inductive proof of the Lagrange Inversion Formula.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
It will be shown that Pascal's Theorem is equivalent to the associativity of a natural binary operation on conic sections. A novel proof for Pascal's Theorem will then be given by showing that this binary operation is associative…
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
We make an attempt at proving the Four Colour Theorem in six pages.