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Disclike lattice reptiles induced by exact polyominoes. (English) Zbl 0987.05041
This paper is devoted to a method of finding a family of \(k\)-piece disclike lattice reptiles. Recall that lattice reptiles homeomorphic to the topological disc in \(\mathbb{R}^2\) are called disclike. This paper can be considered as a first attempt to classify the small piece disclike reptiles. To this end the authors introduce the concept of state graph and exhibit 29 four-piece disclike reptiles derived from tetrominoes.

MSC:
05B50 Polyominoes
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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References:
[1] Bandt C., Proc. Amer. Math. Soc. 112 pp 549– (1991)
[2] Bandt C., J. London Math. Soc. 50 (2) pp 582– (1994)
[3] DOI: 10.1007/BF02574705 · Zbl 0754.05030 · doi:10.1007/BF02574705
[4] DOI: 10.1002/mana.19961780107 · Zbl 0851.52020 · doi:10.1002/mana.19961780107
[5] DOI: 10.1007/BF01194164 · Zbl 0855.05043 · doi:10.1007/BF01194164
[6] Gilbert W. J., Ann. Sc. Math. Quebec 11 pp 65– (1987)
[7] DOI: 10.4153/CJM-1982-093-4 · Zbl 0478.10007 · doi:10.4153/CJM-1982-093-4
[8] DOI: 10.1007/s00041-001-4007-6 · Zbl 0978.28500 · doi:10.1007/s00041-001-4007-6
[9] DOI: 10.1007/BF02249260 · Zbl 0866.52014 · doi:10.1007/BF02249260
[10] DOI: 10.1006/aima.1996.0045 · Zbl 0893.52013 · doi:10.1006/aima.1996.0045
[11] DOI: 10.1007/BF02647948 · Zbl 0893.52015 · doi:10.1007/BF02647948
[12] DOI: 10.1142/S0218348X96000601 · Zbl 0870.68152 · doi:10.1142/S0218348X96000601
[13] DOI: 10.1007/BF01831118 · Zbl 0832.52005 · doi:10.1007/BF01831118
[14] DOI: 10.1137/0406040 · Zbl 0826.52019 · doi:10.1137/0406040
[15] DOI: 10.1016/S0019-9958(84)80007-8 · Zbl 0592.05017 · doi:10.1016/S0019-9958(84)80007-8
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