Related papers: A short proof of Combinatorial Nullstellensatz

In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situation where the original theorem does not seem to work.

We give a short proof of the most general version of the Nullstellensatz without using the Axiom of Choice.

The aim of this note is to present an easy proof of Hilbert's Nullstellensatz using Groebner basis. I believe, that the proof has some methodical advantage in a course on Groebner bases. Key words: Hilbert's Nullstellensatz, Groebner bases.

We present different techniques for applying Combinatorial Nullstellensatz to polynomials over finite fields. For examples, we generalize theorems from Noga Alon's paper on the subject, and present a few of our own.

In this expository note we show how combinatorial Nullstellensatz by N. Alon naturally appears in solutions of elementary problems. Simple ideas gradually and naturally appear in such solutions, thus bringing a reader to generalizations.…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We revisit and further explore the celebrated Combinatorial Nullstellens\"atze of N. Alon in several different directions.

Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of $|f(A,B)|$ for finite subsets $A$, $B$ of a field, and polynomial $f(x,y)$ of the form $f(x,y)=g(x)+yh(x)$, where degree of $g$ is greater then degree…

We give an undergraduate short and simple proof for Zariski's lemma.

We discuss here some computational aspects of the Combinatorial Nullstellensatz argument. Our main result shows that the order of magnitude of the symmetry group associated with permutations of the variables in algebraic constraints,…

By Rabinowitsch' trick Hilbert's Nullstellensatz follows from the weak Nullstellensatz (Rabinowitsch 1929). The weak version can be shown with elimination theory. Hilbert's original proof is also based on successive elimination. Lasker…

Using the Rabinowitsch trick, we prove a version of Nullstellensatz over quaternions, which generalizes Hilbert's Nullstellensatz over complex numbers.

In this expository paper, we present simple proofs of the Classical, Real, Projective and Combinatorial Nullstellens\"atze. Several applications are also presented such as a classical theorem of Stickelberger for solutions of polynomial…

As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the q-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.

Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…

We provide a short proof of the 1-dimensional flat chain conjecture.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We compile a long list of equivalent formulations of Hilbert's Nullstellensatz in infinite dimensions, and prove a persistence result for the strong Nullstellensatz in large polynomial rings.

In this note, we will give a short proof of an identity for cubic partitions.

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the…