On a combinatorial problem of Erdős, Kleitman and Lemke

Details On a combinatorial problem of Erdős, Kleitman and Lemke On a combinatorial problem of Erdős, Kleitman and Lemke

2010-10-25

arxiv.org/abs/1010.5042v1

Mathematics

Combinatorics

13 pages, submitted

Scientific paper

In this paper, we study a combinatorial problem originating in the following conjecture of Erd{o}s and Lemke: out of n divisors of n, repetitions being allowed, one can always find some of them whose sum is n. Even though Kleitman and Lemke could prove this conjecture, they also noticed that more general results of this form could be derived from the investigation of a certain zero-sum invariant, in the context of finite Abelian groups. Building among others on earlier works by Alon and Dubiner and by the author, our main theorem gives a new upper bound for this invariant in the general case, and provides its right order of magnitude.

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