Related papers: A note on the Lee-Yang circle theorem

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

In this note we give a detailed proof of a theorem of Aubin.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches.

This note presents an interesting counterexample to a basic covering problem.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

The note complements topological aspects of the theory of chiral algebras.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.

In a present note we give a new proof of Etingof-Kazhdan quantization theorem.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

A very simple but useful almost sure convergence theorem of probability is given.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

This note contains a short proof of the functional equation for the zeta function.

This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.