Séminaire CAESAR
de combinatoire additive
Séance du jeudi 15 mai 2014
(11 heures, École polytechnique, salle de conférence):
Norbert HEGYVARI
(Eotvos University and Rényi Institute, Budapest, Hongrie)
Recent progress in Hilbert cubes theory: combinatorial aspects of some
ergodic theorems
In 1892, Hilbert defined an affine d-dimensional cube (which is nowadays
called Hilbert cube) as follows: let x_0 be an integer and
a_1 < a_2 <... < a_d be a
sequence of integers. Then the Hilbert cube
H(x_0,a_1,a_2,\dots, a_d) is the set {x_0+{0,a_1}+...+{0,a_d}}.
Hilbert cubes have many applications from Szemerédi theorem to the
distribution of non-residues in the finite field of prime cardinality.
We will discuss some new results and problems in this topic.
In the second half of the talk we give a short proof of a
generalization of Raimi-Hindman's theorem.
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