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Experimental Mathematics Volume 3, 1994 - Issue 4
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Original Articles

Remarks on Self-Affine Tilings

Derek Hacon Departamento de Matemática, PUC-Rio, Rua Marquês de Sāo Vicente, 225, Rio de Janeiro, RJ 22453-900, Brasil E-mail: [email protected]
,
Nicolau C. Saldanha Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-320, Brasil E-mail: [email protected]
&
J. J. P. Veerman Departamento de Matemática, Universidade Federal de Pernambuco, Cidade Universitária, Rua Prof. Luis Freire, Recife, PE, 50740-540 E-mail: [email protected]
Pages 317-327 | Published online: 03 Apr 2012

Citations (21)

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Read on this site (2)

J. J. P. Veerman, L. S. Fox & P. J. Oberly. (2023) A Remarkable Summation Formula, Lattice Tilings, and Fluctuations. The American Mathematical Monthly 130:1, pages 63-75.
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J. J.P. Veerman & B.D. Stošić. (2000) On the Dimensions of Certain Incommensurably Constructed Sets. Experimental Mathematics 9:3, pages 413-423.
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Articles from other publishers (19)

Татьяна Ивановна Зайцева, Tatyana Ivanovna Zaitseva, Владимир Юрьевич Протасов & Vladimir Yur'evich Protasov. (2022) Самоподобные 2-аттракторы и тайлыSelf-affine attractors and tiles. Математический сборник Matematicheskii Sbornik 213:6, pages 71-110.
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Tatyana Ivanovna Zaitseva & Vladimir Yur'evich Protasov. (2022) Self-affine $2$-attractors and tiles. Sbornik: Mathematics 213:6, pages 794-830.
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Lian Wang & King-Shun Leung. (2020) Radix expansions and connectedness of planar self-affine fractals. Monatshefte für Mathematik 193:3, pages 705-724.
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Miklós Hartmann & Tamás Waldhauser. (2017) On strong affine representations of the polycyclic monoids. Semigroup Forum 97:1, pages 87-114.
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Jun Jason Luo & Lian Wang. (2018) Topological properties of self-similar fractals with one parameter. Journal of Mathematical Analysis and Applications 457:1, pages 396-409.
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King-Shun Leung & Jun Jason Luo. (2017) A characterization of connected self-affine fractals arising from collinear digits. Journal of Mathematical Analysis and Applications 456:1, pages 429-443.
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Jingcheng Liu, Sze-Man Ngai & Juan Tao. (2016) Connectedness of a class of two-dimensional self-affine tiles associated with triangular matrices. Journal of Mathematical Analysis and Applications 435:2, pages 1499-1513.
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Gregory R. Conner & Jörg M. Thuswaldner. (2016) Self-affine manifolds. Advances in Mathematics 289, pages 725-783.
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King-Shun Leung & Jun Jason Luo. (2014) Connectedness of planar self-affine sets associated with non-collinear digit sets. Geometriae Dedicata 175:1, pages 145-157.
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Yong Ma, Xin-Han Dong & Qi-Rong Deng. (2014) The connectedness of some two-dimensional self-affine sets. Journal of Mathematical Analysis and Applications 420:2, pages 1604-1616.
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Jing-Cheng Liu, Jun Jason Luo & Heng-wen Xie. (2014) On the connectedness of planar self-affine sets. Chaos, Solitons & Fractals 69, pages 107-116.
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King-Shun Leung & Jun Jason Luo. (2012) Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets. Journal of Mathematical Analysis and Applications 395:1, pages 208-217.
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JianLin Li. (2011) Analysis of a class of spectral pair conditions. Science China Mathematics 54:10, pages 2099-2110.
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Qi-Rong Deng & Ka-sing Lau. (2011) Connectedness of a class of planar self-affine tiles. Journal of Mathematical Analysis and Applications 380:2, pages 493-500.
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King-Shun Leung & Ka-Sing Lau. (2007) Disklikeness of planar self-affine tiles. Transactions of the American Mathematical Society 359:7, pages 3337-3355.
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Shigeki Akiyama & Jörg M. Thuswaldner. (2004) A Survey on Topological Properties of Tiles Related to Number Systems. Geometriae Dedicata 109:1, pages 89-105.
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JUN LUO, HUI RAO & BO TAN. (2012) TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS. Fractals 10:02, pages 223-227.
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Karlheinz Gröchenig, Andrew Haas & Albert Raugi. (1999) Self-Affine Tilings with Several Tiles, I. Applied and Computational Harmonic Analysis 7:2, pages 211-238.
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J. J. P. Veerman. (1995) Intersecting self-similar Cantor sets. Boletim da Sociedade Brasileira de Matem�tica 26:2, pages 167-181.
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