An asymptotically tight bound for the Davenport constant

Benjamin Girard

doi:10.5802/jep.79

An asymptotically tight bound for the Davenport constant
[Une borne asymptotiquement optimale pour la constante de Davenport]

Benjamin Girard ¹

¹ Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathématiques de Jussieu - Paris Rive Gauche, IMJ-PRG F-75005, Paris, France

Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 605-611.

Résumé
Abstract

Nous prouvons que pour tout entier $r \geq 1$ , la constante de Davenport $D (C_{n}^{r})$ est équivalente à $r n$ lorsque $n$ tend vers l’infini. Nous proposons aussi une extension de ce théorème.

We prove that for every integer $r \geq 1$ the Davenport constant $D (C_{n}^{r})$ is asymptotic to $r n$ when $n$ tends to infinity. An extension of this theorem is also provided.

Reçu le : 2018-02-19
Accepté le : 2018-06-24
Publié le : 2018-07-01

MR Zbl

DOI : 10.5802/jep.79

Classification : 05E15, 11B30, 11B75, 11A25, 20D60, 20K01
Keywords: Additive combinatorics, zero-sum sequences, Davenport constant, finite Abelian groups
Mot clés : Combinatoire additive, suites de somme nulle, constante de Davenport, groupes abéliens finis

Affiliations des auteurs :

Benjamin Girard ¹

¹ Sorbonne Université, Université Paris Diderot, CNRS, Institut de Mathématiques de Jussieu - Paris Rive Gauche, IMJ-PRG F-75005, Paris, France

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {An asymptotically tight bound for {the~Davenport} constant},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {605--611},
     publisher = {\'Ecole polytechnique},
     volume = {5},
     year = {2018},
     doi = {10.5802/jep.79},
     zbl = {1401.05311},
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     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.79/}
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Benjamin Girard. An asymptotically tight bound for the Davenport constant. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 605-611. doi : 10.5802/jep.79. https://jep.centre-mersenne.org/articles/10.5802/jep.79/

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