Grynkiewicz, David J. (2005) On a Conjecture of Hamidoune for Subsequence Sums. Integers, 5 (2). A07. ISSN 15531732. http://resolver.caltech.edu/CaltechAUTHORS:GRYint05

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Abstract
Let G be an abelian group of order m, let S be a sequence of terms from G with k distinct terms, let m ∧ S denote the set of all elements that are a sum of some mterm subsequence of S, and let S be the length of S. We show that if S ≥ m + 1, and if the multiplicity of each term of S is at most m − k + 2, then either m ∧ S ≥ min{m, S − m + k − 1}, or there exists a proper, nontrivial subgroup Ha of index a, such that m ∧ S is a union of Hacosets, Ha ⊆ m ∧ S, and all but e terms of S are from the same Hacoset, where e ≤ min{S−m+k−2 Ha − 1, a − 2} and m ∧ S ≥ (e + 1)Ha. This confirms a conjecture of Y. O. Hamidoune.
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Additional Information:  Received: 3/16/04, Revised: 12/24/04, Accepted: 1/6/05, Published: 9/1/05 I would like to thank my advisor R. Wilson for his continual support and understanding, and the referee for several useful suggestions. 
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Deposited On:  16 May 2006 
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