Related papers: Proofs of some Conjectures from the OEIS

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.

We prove the topological analogue of the period-index conjecture in each dimension away from a small set of primes.

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…

In this paper, we give recurrence relations and identities for some integer sequences related to Ward numbers such as Ward-Lah numbers, varied Ward numbers and binomial Ward numbers. Most of the sequences are entered in the On-Line…

We provide new sufficient conditions under which Ryser's conjecture holds.

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the…

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.

We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…

Electronic version of Entry in Encyclopedia of Nonlinear Science.

This paper gives a brief description of the author's database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned.

In this paper, we discuss about some results on average of Fibonacci and Lucas sequences that may be found in the OEIS code A111035.

In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.

A proof of Sendov's conjecture is given.

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…

We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.