scholarly journals Combinatorial Nullstellensatz

1999 ◽  
Vol 8 (1-2) ◽  
pp. 7-29 ◽  
Author(s):  
NOGA ALON
Keyword(s):  
Number Theory ◽  
Graph Theory ◽  
Additive Number Theory ◽  
Graph Colouring ◽  
Combinatorial Nullstellensatz ◽  
Additive Number ◽  
Combinatorial Number Theory ◽  
Algebraic Technique

We present a general algebraic technique and discuss some of its numerous applications in combinatorial number theory, in graph theory and in combinatorics. These applications include results in additive number theory and in the study of graph colouring problems. Many of these are known results, to which we present unified proofs, and some results are new.

scholarly journals On the Possible Orders of a Basis for a Finite Cyclic Group

10.37236/351 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Peter Dukes ◽  
Peter Hegarty ◽  
Sarada Herke
Keyword(s):  
Number Theory ◽  
Graph Theory ◽  
Cyclic Group ◽  
Additive Number Theory ◽  
Exact Results ◽  
Equivalent Problem ◽  
Additive Number ◽  
Finite Cyclic Group

We prove a result concerning the possible orders of a basis for the cyclic group ${\Bbb Z}_n$, namely: For each $k \in {\Bbb N}$ there exists a constant $c_k > 0$ such that, for all $n \in {\Bbb N}$, if $A \subseteq {\Bbb Z}_n$ is a basis of order greater than $n/k$, then the order of $A$ is within $c_k$ of $n/l$ for some integer $l \in [1,k]$. The proof makes use of various results in additive number theory concerning the growth of sumsets. Additionally, exact results are summarized for the possible basis orders greater than $n/4$ and less than $\sqrt{n}$. An equivalent problem in graph theory is discussed, with applications.

Additive Number Theory

Science ◽  
1936 ◽  
Vol 84 (2176) ◽  
pp. 9-9
Author(s):  
Watson Davis
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number

scholarly journals Rectification Principles in Additive Number Theory

1998 ◽  
Vol 19 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Y. F. Bilu ◽  
V. F. Lev ◽  
I. Z. Ruzsa
Keyword(s):  
Number Theory ◽  
Additive Number Theory ◽  
Additive Number
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