Related papers: On three conjectures of P. Barry

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

New cases of the multiplicity conjecture are considered.

In this paper, we prove certain theorems about three consecutive primes.

We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.

We prove Simon's conjecture for 3-manifolds.

We piece together ingredients, which are well known and documented in the literature, into a new proof of the existence of semistable 3-fold flips

We survey recent developments on the Restriction conjecture.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

In this paper, we prove a conjecture of Schnell in the surface case.

In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.

The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note we observe…

An erratum to this article is posted at https://gcc.episciences.org/page/errata This paper generalizes results of M. Moon on the fibering of certain compact 3-manifolds over the circle. It also generalizes a theorem of H. B. Griffiths on…

Here we prove some conjectures on the monotony of combinatorial sequences from the recent preprint of Zhi--Wei Sun.

Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this article, we give a reformulation of a result from Howe, Leprevost and Poonen on a three dimensional family of abelian threefolds. We also link their result to a conjecture of Serre on a precise form of Torelli theorem for genus 3…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

In this paper we present many congruences for several Ap\'ery-like sequences.