Distinct length modular zero-sum subsequences: A proof of Graham's conjecture期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Distinct length modular zero-sum subsequences: A proof of Graham's conjecture

Authors:	Weidong Gao Yahya Ould Hamidoune

Affiliation:	^a Center for Combinatorics, LPMC, Nankai University, Tianjin, 300071, People's Republic of China ^b UPMC Univ. Paris 06, E. Combinatoire, Case 189, 4 Place Jussieu, 75005 Paris, France

Abstract:	Text Let S be a sequence of n nonnegative integers not exceeding n−1 such that S takes at least three distinct values. We show that S has two nonempty zero-sum subsequences with distinct lengths. This proves a conjecture of R.L. Graham. The validity of this conjecture was verified by Erd?s and Szemerédi for all sufficiently large prime n. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=LftJj-E6aQA.

Keywords:	Length of sequence Zero-sum sequence
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