This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [Invent. Math. 44 (1978) 259-264] and the conjecture that the problem is undecidable.
@article{ITA_2008__42_1_21_0,
author = {Margenstern, Maurice},
title = {About the domino problem in the hyperbolic plane from an algorithmic point of view},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {42},
year = {2008},
pages = {21-36},
doi = {10.1051/ita:2007045},
mrnumber = {2382542},
zbl = {pre05302954},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2008__42_1_21_0}
}
Margenstern, Maurice. About the domino problem in the hyperbolic plane from an algorithmic point of view. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) pp. 21-36. doi : 10.1051/ita:2007045. http://gdmltest.u-ga.fr/item/ITA_2008__42_1_21_0/
[1] , The undecidability of the domino problem. Mem. Amer. Math. Soc. 66 (1966) 1-72. | MR 216954 | Zbl 0199.30802
[2] , A strongly aperiodic set of tiles in the hyperbolic plane. Invent. Math. 159 (2005) 119-132. | MR 2142334 | Zbl 1064.52012
[3] , New tools for cellular automata of the hyperbolic plane. J. Univ. Comput. Sci. 6 (2000) 1226-1252. | MR 1817069 | Zbl 0967.68111
[4] , About the domino problem in the hyperbolic plane from an algorithmic point of view2006), available at: http://www.lita.sciences.univ-metz.fr/~margens/hyp_dominoes.ps.gzip
[5] , Fibonacci numbers and words in tilings of the hyperbolic plane. TUCS Gen. Publ. 43 (2007) 36-41.
[6] , About the domino problem in the hyperbolic plane, a new solution, arXiv:cs.CG/0701096 (2007). | MR 2396073
[7] , The domino problem of the hyperbolic plane is undecidable, arXiv:0706.4161 (2007). | MR 2396073 | Zbl 1152.03036
[8] , Cellular Automata in Hyperbolic Spaces, Volume 1, Theory. OCP, Philadelphia (2007). | Zbl 1147.68583
[9] , Undecidability and nonperiodicity for tilings of the plane. Invent. Math. 12 (1971) 177-209. | MR 297572 | Zbl 0197.46801
[10] , Undecidable tiling problems in the hyperbolic plane. Invent. Math. 44 (1978) 259-264. | MR 484409 | Zbl 0359.50011
[11] , Proving theorems by pattern recognition. Bell System Tech. J. 40 (1961) 1-41.