Two finiteness theorems for periodic tilings of d-dimensional euclidean space |
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Authors: | N P Dolbilin A W M Dress D H Huson |
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Institution: | (1) Department of Mathematics, Steklov Institute, Gubkin 8, 117333 Moscow, Russia nikolai@dolbilin.mian.su, RU;(2) FSPM, Bielefeld University, 33501 Bielefeld, Germany {dress,huson}@mathematik.uni-bielefeld.de, DE |
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Abstract: | Consider the d -dimensional euclidean space E
d
. Two main results are presented: First, for any N∈
N, the number of types of periodic equivariant tilings that have precisely N orbits of (2,4,6, . . . ) -flags with respect to the symmetry group Γ , is finite. Second, for any N∈
N, the number of types of convex, periodic equivariant tilings that have precisely N orbits of tiles with respect to the symmetry group Γ , is finite. The former result (and some generalizations) is proved combinatorially, using Delaney symbols, whereas the proof
of the latter result is based on both geometric arguments and Delaney symbols.
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<onlinepub>7 August, 1998
<editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt;
<pdfname>20n2p143.pdf
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Received September 5, 1996, and in revised form January 6, 1997. |
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