Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to
tackle combinatorial problems in diverse areas of mathematics. This book focuses on the …

Abstract A subset AA of an abelian group GG is sequenceable if there is an ordering (a 1,…,
ak) (a_1,...,a_k) of its elements such that the partial sums (s 0, s 1,…, sk) (s_0,s_1,...,s_k) …

Abstract A subset SS of a group (G,+) (G,+) is tt‐weakly sequenceable if there is an ordering
(y 1,…, yk) (y_1,...,y_k) of its elements such that the partial sums s 0, s 1,…, sk …

Using the polynomial method in additive number theory, this article establishes a new
addition theorem for the set of subsums of a set satisfying A∩(− A)=∅ in ℤ/p ℤ …

Let \mathbbF be a field, V⊆\mathbbF^n be a (combinatorially interesting) finite set of points.
Several important properties of V are reflected by the polynomial functions on V. To study …

An additive coloring of a graph G is an assignment of positive integers {1, 2, ..., k\} 1, 2,…, k
to the vertices of G such that for every two adjacent vertices the sums of numbers assigned …

Let Γ be an Abelian group and let G be a simple graph. We say that G is Γ-colorable if for
some fixed orientation of G and every edge labeling ℓ: E (G)→ Γ, there exists a vertex …

We study multivariate polynomials over 'structured'grids. Firstly, we propose an interpretation
as to what it means for a finite subset of a field to be structured; we do so by means of a …

In this article, we use the Combinatorial Nullstellensatz to give new proofs of the Cauchy-
Davenport, the Dias da Silva-Hamidoune and to generalize a previous addition theorem of …

Given a hypergraph $ H=(V, E) $, define for every edge $ e\in E $ a linear expression with
arguments corresponding with the vertices. Next, let the polynomial $ p_H $ be the product …