Related papers: A short proof of the Hilton-Milner Theorem

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather…

The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary…

We reformulate, in the context of continuous logic, an oscillation theorem originally proved by G. Hjorth. We give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view…

The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.

We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety.

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

Recent work of Scott and Wilmer and of Woodroofe extends the Erd\H{o}s-Ko-Rado theorem from set systems to subspaces of k-forms in an exterior algebra. We prove an extension of the Hilton-Milner theorem to the exterior algebra setting,…

According to Chen and Fu's method, we offer a short proof for Dougall's $_2H_2$-series identity.

In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.

We prove a covariant version of the Stinespring theorem for Hilbert C*-modules.

We give a short proof of the duality theorem for the reduced $L_p$-cohomology of a complete oriented Riemannian manifold.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

In this paper we consider some possible approaches to the proof of the Riemann Hypothesis using the Li criterion.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.