Related papers: The Induced Bipartite Ramsey Theorem: An Expositio…

We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.

In this paper, we study the bicomplex version of the Paley-Weiner theorem and the Cauchy integral formula in the upper half-plane.

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

This paper offers a proof of the Coase theorem by formalizing the notion of ideal exchanges.

A classification is given of all the countable homogeneous ordered bipartite graphs.

This is an exposition of Gauss's proof of Descartes's rule of signs.

This is a research announcement of the theory of orbifold quantum cohomology.

A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension,…

Showing that the Ramsey property holds for a class of finite structures can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. In this paper we propose a new strategy to show that a class…

We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\o}lner sequences of non-empty…

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

In contrast to the abundance of "direct" Ramsey results for classes of finite structures (such as finite ordered graphs, finite ordered metric spaces and finite posets with a linear extension), in only a handful of cases we have a…

An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.

A Ramsey-like theorem is a statement of the form ``For every 2-coloring of $[\mathbb{N}]^2$, there exists an infinite set~$H \subseteq \mathbb{N}$ such that $[H]^2$ avoids some pattern''. We prove that none of these statements are…

We settle in the affirmative the Graham-Sloane conjecture.

In this note we give a combinatorial characterization of all the unmixed bipartite graphs.

A generalization of the law of total covariance is presented and proved.