On the Harborth constant of C 3 C 3p
Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 3, pp. 613-633.

Soit (G,+,0) un groupe abélien fini. La constante de Harborth de G, notée g(G), est le plus petit entier k tel que toute suite d’éléments deux à deux distincts de G de longueur k, de manière équivalente tout sous-ensemble de G de cardinal au moins k, admet une sous-suite de longueur exp(G) dont la somme soit 0. Dans cet article, il est démontré que g(C 3 C 3p )=3p+3 pour tout nombre premier p3 et que g(C 3 C 9 )=13.

For a finite abelian group (G,+,0) the Harborth constant g(G) is the smallest integer k such that each squarefree sequence over G of length k, equivalently each subset of G of cardinality at least k, has a subsequence of length exp(G) whose sum is 0. In this paper, it is established that g(C 3 C 3p )=3p+3 for prime p3 and g(C 3 C 9 )=13.

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DOI : https://doi.org/10.5802/jtnb.1097
Classification : 11B30,  20K01
Mots clés : finite abelian group, zero-sum problem, Harborth constant, squarefree sequence
@article{JTNB_2019__31_3_613_0,
     author = {Philippe Guillot and Luz E. Marchan and Oscar Ordaz and Wolfgang A. Schmid and Hanane Zerdoum},
     title = {On the {Harborth} constant of $C_3 \oplus C_{3p}$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {613--633},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {3},
     year = {2019},
     doi = {10.5802/jtnb.1097},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1097/}
}
Philippe Guillot; Luz E. Marchan; Oscar Ordaz; Wolfgang A. Schmid; Hanane Zerdoum. On the Harborth constant of $C_3 \oplus C_{3p}$. Journal de Théorie des Nombres de Bordeaux, Tome 31 (2019) no. 3, pp. 613-633. doi : 10.5802/jtnb.1097. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1097/

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