Related papers: A bijectional attack on the Razumov-Stroganov conj…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.
We give a bijective proof of a conjecture of Regev and Vershik on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection proves a result that is stronger and more symmetric than the original conjecture,…
In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.
This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous territory of the Riemann Hypothesis. We will mostly focus…
We consider Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system is rational too. This assertion confirms…
This article has the sole purpose of presenting a simple, self-contained and direct proof of the fact that the Pak-Stanley labeling is a bijection. The construction behind the proof is subsumed in a forthcoming paper [R. Duarte and A.…
A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.
We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and…
In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.
We expose here a short proof of Cramer's theorem in R based on convex duality.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
In this paper, the abc conjecture is negated under certain conditions
We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.
In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.
In this paper, we study logics of dependence on the propositional level. We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well…
We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices and $e$ edges, where $v\le e$, and write $M(G)=2e(G)$. We…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In the paper different kinds of proof of a given statement are discussed. Detailed descriptions of direct and indirect methods of proof are given. Logical models illustrate the essence of specific types of indirect proofs. Direct proofs of…