Related papers: On some conjectures of P. Barry

We prove a conjecture due to Y. Last on Jacobi matrices.

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…

We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…

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

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

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…

In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We reprove a few results concerning paperfolding sequences using properties of Catalan numbers modulo 2.

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least…

WITHDRAWN: The proof contains an uncorrectable gap in the proof of theorem 7 on page 11. A proof of the Krzyz conjecture is presented, based on the application of the variational method, as well as on the use of two classical results and…

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

We present two related conjectures, arising in work on i-matchings in random r-regular bipartite graphs. The conjectures themselves are easily stated and involve only basic properties of convergent power series. One formulation involves…

We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding…