Topological Properties of a Class of Higher-dimensional Self-affine Tiles
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 727-740
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We construct a family of self-affine tiles in $\mathbb{R}^{d}$ ($d\geqslant 2$) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in $\mathbb{R}^{2}$, and its extension to $\mathbb{R}^{3}$ by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.
Deng, Guotai; Liu, Chuntai; Ngai, Sze-Man. Topological Properties of a Class of Higher-dimensional Self-affine Tiles. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 727-740. doi: 10.4153/S0008439519000237
@article{10_4153_S0008439519000237,
author = {Deng, Guotai and Liu, Chuntai and Ngai, Sze-Man},
title = {Topological {Properties} of a {Class} of {Higher-dimensional} {Self-affine} {Tiles}},
journal = {Canadian mathematical bulletin},
pages = {727--740},
year = {2019},
volume = {62},
number = {4},
doi = {10.4153/S0008439519000237},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000237/}
}
TY - JOUR AU - Deng, Guotai AU - Liu, Chuntai AU - Ngai, Sze-Man TI - Topological Properties of a Class of Higher-dimensional Self-affine Tiles JO - Canadian mathematical bulletin PY - 2019 SP - 727 EP - 740 VL - 62 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000237/ DO - 10.4153/S0008439519000237 ID - 10_4153_S0008439519000237 ER -
%0 Journal Article %A Deng, Guotai %A Liu, Chuntai %A Ngai, Sze-Man %T Topological Properties of a Class of Higher-dimensional Self-affine Tiles %J Canadian mathematical bulletin %D 2019 %P 727-740 %V 62 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000237/ %R 10.4153/S0008439519000237 %F 10_4153_S0008439519000237
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