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

An elementary proof of an identity by Lyons, Paule and Riese is given. It is simpler than all the 3 published proofs.

Stirling's formula is a powerful asymptotic approximation of the factorial function. Many well-known proofs of this formula are grounded in integral calculus. In this paper, we present an alternative proof of Stirling's formula using only…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We prove a local version of the Mazur-Ulam theorem.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.

The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

We give a short proof of Ahlfors' theorem on covering surfaces.

Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.