On weighted sums in abelian groups

✍ Scribed by Y.O. Hamidoune

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 225 KB
• Volume: 162
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00281-z

✦ Synopsis

Let G be an abelian group of order n and Davenport constant d and let k be a natural number. Let Xo, xl, ..., x m be a sequence of elements of G such that x o has the most repeated value in the sequence. Let {wi; 1 <<, i <~ k} be a family of integers prime relative to n. We obtain the following two generalizations of the Erd~Ss~inzburg-Ziv Theorem.

For rn >/n + k -1, we prove that there is a permutation ct of [1, m] such that l<~i~k l~i<~k

For k >/n -1 and m >/k + d -l, we prove that there is a k-subset K ~ [1,m] such that ~ x i = kx o.