Related papers: Summary on the proof of BAB Conjecture

A main purpose of this paper is to prove that the class of finite dimensional algebras which verify Han's conjecture is closed under split bounded extensions.

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.

In the recent past, the reduction-based and the model-based methods to prove cut elimination have converged, so that they now appear just as two sides of the same coin. This paper details some of the steps of this transformation.

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.

The paper presents a counterexample to the Hodge conjecture.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…

We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.

Remarks on mathematical proof and the practice of mathematics.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand the main results.

A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered

The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof…

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…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…

In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.