Related papers: A short proof of Combinatorial Nullstellensatz

We present in this work a new and simple proof of the false centre theorem.

I give a short and completely elementary proof of Takagi's 1921 theorem on the zeros of a composite polynomial $f(d/dz) \, g(z)$.

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

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

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…

We describe two distinct simple, short and self contained proofs of the composition lemma.

This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.

In this note we give a detailed proof of a theorem of Aubin.

In this paper, we give a simple counter example to the famous Hodge conjecture.

This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).

We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebraically closed. We also show that every division ring can be…

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…

Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided

We prove a version of $Z$-set unknotting theorem for uncountable products of real numbers.

For a finite set $\cal F$ of polynomials over fixed finite prime field of size $p$ containing all polynomials $x^2 - x$ a Nullstellensatz proof of the unsolvability of the system $$ f = 0\ ,\ \mbox{ all } f \in {\cal F} $$ in the field is a…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.