Related papers: On a conjecture by Blocki-Zwonek
We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
We prove a conjecture by D. Zeilberger on the determinant of a certain matrix and relate it to a problem of non-existence of 1-cycles in this note.
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on $7222$ vertices, and is built on the recent work of Hollom (2024).
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.
We settle in the affirmative the Graham-Sloane conjecture.
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
This note is concerned with the disproof of the most general case of Parker's conjecture. The conjecture relates a certain group theoretic objects to the field of moduli of a Dessin d'enfant.
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
We develop techniques to deal with monotonicity of sequences z_{n+1}/z_n and \sqrt[n]{z_n}. A series of conjectures of Zhi-Wei Sun and of Amdeberhan et al. are verified in certain unified approaches.
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 present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.
This is a companion note to our paper 'Some advances on Sidorenko's conjecture', elaborating on a remark in that paper that the approach which proves Sidorenko's conjecture for strongly tree-decomposable graphs may be extended to a broader…
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.
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.