Parallelepipeds, Nilpotent Groups, and Gowers Norms

Details Parallelepipeds, Nilpotent Groups, and Gowers Norms Parallelepipeds, Nilpotent Groups, and Gowers Norms

2006-05-31

arxiv.org/abs/math/0606004v1

Mathematics

Combinatorics

Scientific paper

In his proof of Szemeredi's Theorem, Gowers introduced certain norms that are
defined on a parallelepiped structure. A natural question is on which sets a
parallelepiped structure (and thus a Gowers norm) can be defined. We focus on
dimensions 2 and 3 and show when this possible, and describe a correspondence
between the parallelepiped structures nilpotent groups.

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