29 citations · 119 across the 13 of their papers we have counts for
6 papers · 1 filter
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…
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…