On a conjecture of Kleitman and Lemke (Q1801584)
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scientific article; zbMATH DE number 205457
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a conjecture of Kleitman and Lemke |
scientific article; zbMATH DE number 205457 |
Statements
On a conjecture of Kleitman and Lemke (English)
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21 February 1994
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Let \(G\) be a finite abelian group of \(N\) elements. The author shows that every sequence of \(N\) elements of \(G\) contains a subsequence \(g_ 1,g_ 2,\dots,g_ r\) with vanishing sum and satisfying \(\sum_ i 1/\text{ord}(g_ i)\) \(\leq 1\). This confirms a conjecture of \textit{D. Kleitman} and \textit{P. Lemke} [J. Number Theory 31, 335--345 (1989; Zbl 0672.10038)] in the abelian case.
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finite abelian group
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sequence
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