Parallelepipeds, Nilpotent Groups, and Gowers Norms

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112980In 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.CombinatoricsDynamical Systems11B75Parallelepipeds, Nilpotent Groups, and Gowers Normstext