An asymptotically tight bound for the Davenport constant

Girard, Benjamin

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

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

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

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

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