期刊论文

Deng, Guotai

英文

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES

0008-4395

2019

62

4

727-740

10.4153/S0008439519000237

Received by the editors October 22, 2018; revised February 14, 2019. Published online on Cambridge Core August 30, 2019. Author G. T. D. was supported by the Fundamental Research Funds for the Central Universities CCNU19TS071. Author C. T. L. was supported in part by the National Natural Science Foundation of China grant 11601403, China Scholarship Council and Research and Innovation Initiatives of WHPU 2018Y18. Author S. M. N. was supported in part by the National Natural Science Foundation of China grants 11771136 and 11271122, the Hunan Province Hundred Talents Program, Construct Program of the Key Discipline in Hunan Province, and a Faculty Research Scholarly Pursuit Funding from Georgia Southern University. AMS subject classification: 28A80, 52C22, 05B45, 51M20. Keywords: self-aõne tile, connectedness, ball-like tile.

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We construct a family of self-affine tiles in ℝd (d ≥ 2) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in ℝ2, and its extension to ℝ3 by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible. ©...