2007/04/04 by Yahya Ould Hamidoune, Hamidoune, Y. O., Anna Lladó +3
Engineering · Mathematics · #11B75 #20D60 #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0704.0541
openalex publication_date 2007/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subset X of an abelian G is said to be \em complete if every element of the subgroup generated by X can be expressed as a nonempty sum of distinct elements from X. Let A⊂ \Zn be such that all the elements of A are coprime with n. Solving a conjecture of Erdős and Heilbronn, Olson proved that A is complete if n is a prime and if |A|>2√(n). Recently Vu proved that there is an absolute constant c, such that for an arbitrary large n, A is complete if |A|≥ c√(n), and conjectured that 2 is essentially the right value of c. We show that A is complete if |A|> 1+2√(n-4), thus proving the last conjecture.