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Tiling with arbitrary tiles
Author(s) -
Gruslys Vytautas,
Leader Imre,
Tan Ta Sheng
Publication year - 2016
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdw017
Subject(s) - tile , mathematics , conjecture , partition (number theory) , combinatorics , discrete mathematics , art , visual arts
Let T be a tile in Z n , meaning a finite subset of Z n . It may or may not tile Z n , in the sense of Z n having a partition into copies of T . However, we prove that T does tile Z d for some d . This resolves a conjecture of Chalcraft.