Séminaire CAESAR
de combinatoire additive
Séance du vendredi 2 décembre 2011
(14 heures, Jussieu, couloir 1525, salle 101):
Simon GRIFFITHS
(IMPA, Rio de Janeiro, Brésil)
Tight bounds on subset sums in abelian groups
Given a subset S of an abelian group G we consider
Z, the set of subset sums of S in G. In a seminal article,
Erdos and Heilbronn proved that every subset S of Z/pZ, for p a prime,
with cardinality at least 3\sqrt{6}\sqrt{p}, has Z=Z/pZ.
This result was later strengthened by Olson (who replaced the constant
by 2) and further sharpened by Dias da Silva and Hamidoune. Olson's
result relied on proving that for every subset S of Z/pZ such that
S and -S are intersection-free, the cardinality of Z is >
min {|S|(|S|+1)/2,p/2}. In this talk we discuss a generalisation
of this result to subsets of arbitrary abelian groups.
(Joint work with Eric Balandraud, Benjamin Girard and Yahya ould
Hamidoune)
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