Published September 2005
| Published
Journal Article
Open
On a Conjecture of Hamidoune for Subsequence Sums
- Creators
- Grynkiewicz, David J.
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.
Additional Information
© 2005 The Author(s). 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.Attached Files
Published - GRYint05.pdf
Files
GRYint05.pdf
Files
(334.0 kB)
Name | Size | Download all |
---|---|---|
md5:e9ea19f9f6e558e17c694416fa66a717
|
334.0 kB | Preview Download |
Additional details
- Eprint ID
- 3126
- Resolver ID
- CaltechAUTHORS:GRYint05
- Created
-
2006-05-16Created from EPrint's datestamp field
- Updated
-
2020-05-18Created from EPrint's last_modified field