Treffer: On a combinatorial problem of Erdős, Kleitman and Lemke
Title:
On a combinatorial problem of Erdős, Kleitman and Lemke
Authors:
Contributors:
Girard, Benjamin
Source:
Advances in Mathematics. 231:1843-1857
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2012.
Publication Year:
2012
Subject Terms:
Finite abelian groups, Mathematics(all), cross number, Group Theory (math.GR), 0102 computer and information sciences, 01 natural sciences, Extremal combinatorics, Zero-sum sequences, Cross number, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), 0101 mathematics, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], Mathematics - Number Theory, Arithmetic functions, related numbers, inversion formulas, Combinatorial aspects of groups and algebras, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], zero-sum sequences, Other combinatorial number theory, Finite Abelian groups, extremal combinatorics, Combinatorics (math.CO), finite Abelian groups, Mathematics - Group Theory, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Document Type:
Fachzeitschrift
Article
File Description:
application/xml; application/pdf
Language:
English
ISSN:
0001-8708
DOI:
10.1016/j.aim.2012.06.025
DOI:
10.48550/arxiv.1010.5042
Access URL:
http://arxiv.org/abs/1010.5042
https://zbmath.org/6094100
https://doi.org/10.1016/j.aim.2012.06.025
https://ui.adsabs.harvard.edu/abs/2010arXiv1010.5042G/abstract
http://export.arxiv.org/pdf/1010.5042
https://arxiv.org/pdf/1010.5042v2
https://www.sciencedirect.com/science/article/pii/S0001870812002526
https://arxiv.org/abs/1010.5042
https://core.ac.uk/display/82189906
https://hal.science/hal-00529045v2
https://hal.science/hal-00529045v2/document
https://zbmath.org/6094100
https://doi.org/10.1016/j.aim.2012.06.025
https://ui.adsabs.harvard.edu/abs/2010arXiv1010.5042G/abstract
http://export.arxiv.org/pdf/1010.5042
https://arxiv.org/pdf/1010.5042v2
https://www.sciencedirect.com/science/article/pii/S0001870812002526
https://arxiv.org/abs/1010.5042
https://core.ac.uk/display/82189906
https://hal.science/hal-00529045v2
https://hal.science/hal-00529045v2/document
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....ef7e6c23e924c32c1bf9acee7e734964
Database:
OpenAIRE
Weitere Informationen
In this paper, we study a combinatorial problem originating in the following conjecture of Erdos and Lemke: given any sequence of n divisors of n, repetitions being allowed, there exists a subsequence the elements of which are summing to n. This conjecture was proved by Kleitman and Lemke, who then extended the original question to a problem on a zero-sum invariant in the framework 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.
15 pages