An addition theorem and maximal zero-sum free sets in Z/pZ

Details An addition theorem and maximal zero-sum free sets in Z/pZ An addition theorem and maximal zero-sum free sets in Z/pZ

2009-07-20

arxiv.org/abs/0907.3492v1

Mathematics

Number Theory

Scientific paper

Using the polynomial method in additive number theory, this article establishes a new addition theorem for the set of subsums of a set satisfying $A\cap(-A)=\emptyset$ in $\mathbb{Z}/p\mathbb{Z}$: \[|\Sigma(A)|\geqslant\min{p,1+\frac{|A|(|A|+1)}{2}}.\] The proof is similar in nature to Alon, Nathanson and Ruzsa's proof of the Erd\"os-Heilbronn conjecture (proved initially by Dias da Silva and Hamidoune \cite{DH}). A key point in the proof of this theorem is the evaluation of some binomial determinants that have been studied in the work of Gessel and Viennot. A generalization to the set of subsums of a sequence is derived, leading to a structural result on zero-sum free sequences. As another application, it is established that for any prime number $p$, a maximal zero-sum free set in $\mathbb{Z}/p\mathbb{Z}$ has cardinality the greatest integer $k$ such that \[\frac{k(k+1)}{2}

Affiliated with

Also associated with

No associations

Rating

An addition theorem and maximal zero-sum free sets in Z/pZ 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 An addition theorem and maximal zero-sum free sets in Z/pZ, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An addition theorem and maximal zero-sum free sets in Z/pZ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-174519