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On a Conjecture of Hamidoune for Subsequence Sums

Grynkiewicz, David J. (2005) On a Conjecture of Hamidoune for Subsequence Sums. Integers, 5 (2). A07. ISSN 1553-1732. 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 m-term 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 Ha-cosets, Ha ⊆ m ∧ S, and all but e terms of S are from the same Ha-coset, 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.


Item Type:Article
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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Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GRYint05
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ID Code:3126
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:16 May 2006
Last Modified:26 Dec 2012 08:52

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