Séminaire CAESAR
de combinatoire additive
Séance du 16 février 2012
(11 heures, Jussieu, couloir 1525, salle 101):
Christian ELSHOLTZ
(TU Graz, Autriche)
Iterated sumsets in the set of squares
Let a_0, a_1,..., a_d be integers.
A Hilbert cube of dimension d is an iterated sumset of the form
H(a_0; a_1,..., a_d) =a_0+{0,a_1} + {0,a_2} + ... + {0, a_d}.
We present a new method to give upper bounds of the dimension of
Hilbert cubes in certain sets. As a special case
we improve Hegyvári and Sárkozy's
upper bound O((log N)^{1/3}) for the maximal dimension of
a Hilbert cube in the set of squares
in $[1,N]$ to O((log log N)^2).
This is a joint work with Rainer Dietmann.
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