Arithmetic sets in groups

DOI10.1007/S00209-018-2125-YzbMath1445.05024arXiv1412.0308OpenAlexW2962749907MaRDI QIDQ2312833

Damiano Fulghesu, Azer Akhmedov

Publication date: 18 July 2019

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0308

zbMATH Keywords

abelian grouparithmetic setCoven-Meyerowitz conjecturenon-abelian free grouptiles in groups

Mathematics Subject Classification ID

Free nonabelian groups (20E05) Special aspects of infinite or finite groups (20F99) Combinatorial aspects of tessellation and tiling problems (05B45) Abelian groups (20K99)

Cites Work

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• On Fuglede's conjecture and the existence of universal spectra
• Direct sum subset decompositions of Z
• Tesselation of integers
• Tiling the integers with translates of one finite set
• Translational tilings of the integers with long periods
• Commuting self-adjoint partial differential operators and a group theoretic problem
• Fuglede's conjecture is false in 5 and higher dimensions
• Tiling the line with translates of one tile
• Fuglede’s conjecture fails in dimension 4

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