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On the Steinhaus tiling problem
Author(s) -
Kolountzakis Mihail N.,
Wolff Thomas
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007750
Subject(s) - mathematics , combinatorics , square tiling , point (geometry) , lattice (music) , finite set , set (abstract data type) , hexagonal tiling , pure mathematics , geometry , mathematical analysis , grid , computer science , physics , acoustics , programming language
Several results are proved related to a question of Steinhaus: is there a set E ⊂ℝ 2 such that the image of E under each rigid motion of IR2 contains exactly one lattice point? Assuming measurability, the analogous question in higher dimensions is answered in the negative, and on the known partial results in the two dimensional case are improved on. Also considered is a related problem involving finite sets of rotations.