On n-sum of an abelian group of order n

2013/08/11 by Weidong Gao, Xia, Xingwu, Gao, Weidong
Computer Science · Engineering · #11B #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1308.2365

openalex publication_date 2013/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be an additive finite abelian group of order n, and let S be a sequence of n+k elements in G, where k≥ 1. Suppose that S contains t distinct elements. Let ∑_n(S) denote the set that consists of all elements in G which can be expressed as the sum over a subsequence of length n. In this paper we prove that, either 0∈ ∑_n(S) or |∑_n(S)|≥ k+t-1. This confirms a conjecture by Y.O. Hamidoune in 2000.

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