Related papers: A double-inductive proof of Moessner's theorem
A very simple but useful almost sure convergence theorem of probability is given.
In this short note I restate and simplify the proof of the impossibility of probabilistic induction from Popper (1992). Other proofs are possible (cf. Popper (1985)).
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…
In this article we use the Desargues' theorem and its reciprocal to solve two problems.
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
We present a new, elementary, dynamical proof of the prime number theorem.
We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.
We prove the Aharoni Berger Conjecture
We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.