Small Doubling and Additive Structure Modulo a Prime

Details Small Doubling and Additive Structure Modulo a Prime Small Doubling and Additive Structure Modulo a Prime

2012-04-14

arxiv.org/abs/1204.3179v1

Mathematics

Combinatorics

9 pages, 29 references

Scientific paper

Let $\emptyset\neq A,B\subseteq{\mathbb{Z}}/p{\mathbb{Z}}$, where $p$ is a prime. The Cauchy-Davenport theorem gives a lower bound for the number of distinct sums $a+b$, where $a\in A$ and $b\in B$. The corresponding inverse theorem, due to Vosper, determines the structure of $A$ and $B$ if the lower bound is attained. A generalization of Vosper's theorem was conjectured by Hamidoune, Serra, and Z\'{e}mor in 2006. We prove that this conjecture is indeed correct. This is known to give a fairly good answer to the $3k-3$ problem in ${\mathbb{Z}}/p{\mathbb{Z}}$.

Affiliated with

Also associated with

No associations

Rating

Small Doubling and Additive Structure Modulo a Prime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Small Doubling and Additive Structure Modulo a Prime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small Doubling and Additive Structure Modulo a Prime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-33529