29 citations · 119 across the 13 of their papers we have counts for
13 papers
Higher Degree Davenport Constants over Finite Commutative Rings
Yair Caro, Benjamin Girard, John R. Schmitt
We generalize the notion of Davenport constants to a `higher degree' and obtain various lower and upper bounds, which are sometimes exact as is the case for certain finite commutat…
On additive bases in infinite abelian semigroups
Pierre-Yves Bienvenu, Benjamin Girard, Thái Hoàng Lê
Building on previous work by Lambert, Plagne and the third author, we study various aspects of the behavior of additive bases in infinite abelian groups and semigroups. We show tha…
Inverse zero-sum problems for certain groups of rank three
Benjamin Girard, Wolfgang Schmid
The inverse problem associated to the Erdős-Ginzburg-Ziv constant and the -constant is solved for finite abelian groups of the form where $n \ge 2…
Direct zero-sum problems for certain groups of rank three
Benjamin Girard, Wolfgang Schmid
We determine the exact value of the -constant and the multiwise Davenport constants for finite abelian groups of rank three having the form $G \simeq C_2 \oplus C_{n_2} \oplus C…
An asymptotically tight bound for the Davenport constant
Benjamin Girard
We prove that for every integer the Davenport constant is asymptotic to when tends to infinity. An extension of this theorem is also provided…
A nullstellensatz for sequences over F_p
Eric Balandraud, Benjamin Girard
Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0.…
Subset sums in abelian groups
Eric Balandraud, Benjamin Girard, Simon Griffiths +1
Denoting by Sigma(S) the set of subset sums of a subset S of a finite abelian group G, we prove that |Sigma(S)| >= |S|(|S|+2)/4-1 whenever S is symmetric, |G| is odd and Sigma(S) i…
k-Sums in abelian groups
Benjamin Girard, Simon Griffiths, Yahya Ould Hamidoune
Given a finite subset A of an abelian group G, we study the set k \wedge A of all sums of k distinct elements of A. In this paper, we prove that |k \wedge A| >= |A| for all k in {2…
On a combinatorial problem of Erdos, Kleitman and Lemke
Benjamin Girard
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…
On the existence of zero-sum subsequences of distinct lengths
Benjamin Girard
In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups. Our…
Inverse zero-sum problems in finite Abelian p-groups
Benjamin Girard
In this paper, we study the minimal number of elements of maximal order within a zero-sumfree sequence in a finite Abelian p-group. For this purpose, in the general context of fini…
Inverse zero-sum problems and algebraic invariants
Benjamin Girard
In this article, we study the maximal cross number of long zero-sumfree sequences in a finite Abelian group. Regarding this inverse-type problem, we formulate a general conjecture…
A new upper bound for the cross number of finite Abelian groups
Benjamin Girard
In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number…