Related papers: Proofs of some Conjectures from the OEIS

We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.

The Online Encyclopedia of Integer Sequences (OEIS) is made up of thousands of numerical sequences considered particularly interesting by some mathematicians. The graphic representation of the frequency with which a number n as a function…

In this article we determine the implicational fragments of most of the known subintuitionistic logics.

We survey recent developments on the Restriction conjecture.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…

New cases of the multiplicity conjecture are considered.

I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…

Integrated organic inference (IOI) is discussed in a concise and informal way with the aim that the reader is given the gist of what this approach to statistical inference is about as well as given pointers to further reading.

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

In this electronic appendix to our paper "Input Invariants," accepted at ESEC/FSE'22, we provide additional examples, formal definitions, theorems, and proof sketches to complement our paper. Furthermore, we show the invariants that ISLearn…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

In this largely expository paper, we will present a list of En -operads and give complete, and in some cases new, proofs of the equivalences between these operads.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

An technically interesting proof of a known theorem.

In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.

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