@article{P:penrose, author = {Penrose, R.}, journal = {The Institute of Mathematics and its Applications Bulletin}, keywords = {fractals, tilings}, month = jul, pages = {266--271}, posted-at = {2005-11-05 09:06:00}, priority = {0}, title = {{The R\^ole of aesthetics in pure and applied mathematical research}}, volume = {10}, year = {1974} } @techreport{B:ammann-beenker, author = {Beenker, F. P. M}, title = {Algebraic theory of non-periodic tilings of the plane by two simple building blocks: a square and a rhombus}, school = {Eindhoven University of Technology}, institution = {Eindhoven University of Technology}, address = {the Netherlands}, type = {TH-Report}, number = {82-WSK04}, year = {1982}, } @article{S:nobel, title = {Metallic Phase with Long-Range Orientational Order and No Translational Symmetry}, author = {Shechtman, D. and Blech, I. and Gratias, D. and Cahn, J. W.}, journal = {Phys. Rev. Lett.}, volume = {53}, issue = {20}, pages = {1951--1953}, numpages = {0}, year = {1984}, month = {Nov}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.53.1951}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.53.1951} } @article{BKSZ:projection, AUTHOR = {Baake, M. and Kramer, P. and Schlottmann, M. and Zeidler, D.}, TITLE = {Planar patterns with fivefold symmetry as sections of periodic structures in {$4$}-space}, JOURNAL = {Internat. J. Modern Phys. B}, FJOURNAL = {International Journal of Modern Physics B. Condensed Matter Physics. Statistical Physics. Applied Physics}, VOLUME = {4}, YEAR = {1990}, PAGES = {2217--2268}, ISSN = {0217-9792}, MRCLASS = {52C20 (52C07 82D25)}, MRNUMBER = {1086074 (92b:52041)}, MRREVIEWER = {Marjorie Senechal}, DOI = {10.1142/S0217979290001054}, URL = {http://dx.doi.org/10.1142/S0217979290001054}, } @unpublished{R:subrosa, author = {Rissanen, M.}, title = {Sub Rosa, a System of Non-Periodic Rhombic Substitution Tilings}, note = {Unpublished}, year = {2013}, } @article {R:mixed-subs, AUTHOR = {Rust, D.}, TITLE = {An uncountable set of tiling spaces with distinct cohomology}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = {205}, YEAR = {2016}, PAGES = {58--81}, ISSN = {0166-8641}, MRCLASS = {37B10 (37B50 54H20 55N05)}, MRNUMBER = {3493307}, DOI = {10.1016/j.topol.2016.01.020}, URL = {http://dx.doi.org/10.1016/j.topol.2016.01.020}, } @book{BG:book, AUTHOR = {Baake, M. and Grimm, U.}, TITLE = {Aperiodic Order. Volume 1: A Mathematical Invitation}, SERIES = {Encyclopedia Math. Appl.}, VOLUME = {149}, PUBLISHER = {Cambridge Univ. Press}, YEAR = {2013}, PAGES = {xvi+531}, ISBN = {978-0-521-86991-1}, MRCLASS = {52-02 (11H06 20Cxx 20H15 82D25)}, MRNUMBER = {3136260}, } @article{MSRRSB:lasers, author = {Mikhael, Jules and Schmiedeberg, Michael and Rausch, Sebastian and Roth, Johannes and Stark, Holger and Bechinger, Clemens}, title = {Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields}, volume = {107}, pages = {7214-7218}, year = {2010}, doi = {10.1073/pnas.0913051107}, abstract ={Quasicrystals provide a fascinating class of materials with intriguing properties. Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most quasicrystals hold 5- or 10-fold symmetry but no single example with 7- or 9-fold symmetry has ever been observed. Here we report on geometrical constraints which impede the formation of quasicrystals with certain symmetries in a colloidal model system. Experimentally, colloidal quasicrystals are created by subjecting micron-sized particles to two-dimensional quasiperiodic potential landscapes created by n = 5 or seven laser beams. Our results clearly demonstrate that quasicrystalline order is much easier established for n = 5 compared to n = 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high-symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e.g., 7-fold symmetry.}, URL = {http://www.pnas.org/content/107/16/7214.abstract}, eprint = {http://www.pnas.org/content/107/16/7214.full.pdf+html}, journal = {Proceedings of the National Academy of Sciences}, } @inproceedings{G:shield, author={G\"{a}hler, F.}, title={Crystallography of Dodecagonal Quasicrystals}, booktitle={Quasicrystalline materials}, note={Proceedings of the I.L.L./CODEST workshop, Grenoble, 21-25 March 1988}, editor={Janot, C. and Dubois, J.M.}, organization={Institut Laue-Langevin, Committee for the Development in Europe of Science and Technology}, isbn={9789971506315}, year={1988}, publisher={World Scientific}, } @article{S:socolar, title = {Simple octagonal and dodecagonal quasicrystals}, author = {Socolar, Joshua E. S.}, journal = {Phys. Rev. B}, volume = {39}, issue = {15}, pages = {10519--10551}, numpages = {0}, year = {1989}, month = {May}, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.39.10519}, url = {http://link.aps.org/doi/10.1103/PhysRevB.39.10519}, } @article{WSI:dodecagonal, author = {Watanabe, Y. and Soma, T. and Ito, M.}, title = {A new quasiperiodic tiling with dodecagonal symmetry}, journal = {Acta Crystallographica Section A}, year = {1995}, volume = {51}, pages = {936--942}, month = {Nov}, doi = {10.1107/S0108767395009160}, url = {http://dx.doi.org/10.1107/S0108767395009160}, } @article{K:parallelograms, author = {Richard Kenyon}, title = {Tiling a Polygon with Parallelograms}, journal = {Algorithmica}, volume = {9}, year = {1993}, pages = {382-397}, ee = {http://dx.doi.org/10.1007/BF01228510}, } @article{KS:parallelograms, author = {Kannan, Sampath and Soroker, Danny}, title = {Tiling Polygons with Parallelograms}, journal = {Discrete Comput. Geom.}, issue_date = {1992}, volume = {7}, month = mar, year = {1992}, issn = {0179-5376}, pages = {175--188}, numpages = {14}, url = {http://dx.doi.org/10.1007/BF02187834}, doi = {10.1007/BF02187834}, acmid = {149144}, publisher = {Springer-Verlag New York, Inc.}, address = {Secaucus, NJ, USA}, } @article{GKM:search, AUTHOR = {G{\"a}hler, Franz and Kwan, Eugene E. and Maloney, Gregory R.}, TITLE = {A computer search for planar substitution tilings with {$n$}-fold rotational symmetry}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {53}, YEAR = {2015}, PAGES = {445--465}, ISSN = {0179-5376}, MRCLASS = {37B10 (37B50 52C23 54H20 55N05)}, MRNUMBER = {3316232}, DOI = {10.1007/s00454-014-9659-5}, URL = {http://dx.doi.org/10.1007/s00454-014-9659-5}, } @article{LB:binary, AUTHOR = {Lan{\c{c}}on, F. and Billard, L.}, TITLE = {Two-dimensional system with a quasicrystalline ground state}, JOURNAL = {J. Physique}, FJOURNAL = {Le Journal de Physique}, VOLUME = {49}, YEAR = {1988}, PAGES = {249--256}, ISSN = {0302-0738}, CODEN = {JOPQAG}, MRCLASS = {82A57 (51M20 52A45)}, MRNUMBER = {933982 (89m:82057)}, MRREVIEWER = {Hanna Nencka}, } @article{G:multi, AUTHOR = {Garc{\'{\i}}a Escudero, Juan}, TITLE = {Random tilings of spherical 3-manifolds}, JOURNAL = {J. Geom. Phys.}, FJOURNAL = {Journal of Geometry and Physics}, VOLUME = {58}, YEAR = {2008}, PAGES = {1451--1464}, ISSN = {0393-0440}, CODEN = {JGPHE5}, MRCLASS = {52C22 (52C23 60D05 92E99)}, MRNUMBER = {2463804 (2010c:52026)}, DOI = {10.1016/j.geomphys.2008.05.015}, URL = {http://dx.doi.org/10.1016/j.geomphys.2008.05.015}, } @article{G:fivefold, AUTHOR = {Garc{\'{\i}}a Escudero, Juan}, TITLE = {Randomness and topological invariants in pentagonal tiling spaces}, JOURNAL = {Discrete Dyn. Nat. Soc.}, FJOURNAL = {Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal}, YEAR = {2011}, PAGES = {Art. ID 946913, 23}, ISSN = {1026-0226}, MRCLASS = {52C20 (37B50 55N05)}, MRNUMBER = {2812547 (2012k:52051)}, MRREVIEWER = {Samuel Petite}, } @article {DN:n-fold, AUTHOR = {Nischke, K.-P. and Danzer, L.}, TITLE = {A construction of inflation rules based on {$n$}-fold symmetry}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {15}, YEAR = {1996}, PAGES = {221--236}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52C20}, MRNUMBER = {1368275 (96j:52035)}, MRREVIEWER = {Richard Kenyon}, DOI = {10.1007/BF02717732}, URL = {http://dx.doi.org/10.1007/BF02717732}, } @mastersthesis {F:thesis, AUTHOR = {Frettl\"{o}h, D.}, TITLE = {Inflation\"{a}re {P}flasterungen der {E}bene mit ${D}_{2m+1}$-{S}ymmetrie und minimaler {M}usterfamilie}, SCHOOL = {Universit\"{a}t Dortmund}, YEAR = {1998}, TYPE = {Diploma {T}hesis}, LANGUAGE = {german}, TRANSLATION = {0}, URL = {http://www.math.uni-bielefeld.de/~frettloe/papers/diplom.pdf} } @article {AP, AUTHOR = {Anderson, J. E. and Putnam, I. F.}, TITLE = {Topological invariants for substitution tilings and their associated {$C^*$}-algebras}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {18}, YEAR = {1998}, PAGES = {509--537}, ISSN = {0143-3857}, MRCLASS = {46L55 (19K99 37B50 54H20)}, MRNUMBER = {1631708 (2000a:46112)}, MRREVIEWER = {G. A. Noskov}, DOI = {10.1017/S0143385798100457}, URL = {http://dx.doi.org/10.1017/S0143385798100457}, } @book {S:book, AUTHOR = {Sadun, L.}, TITLE = {Topology of Tiling Spaces}, SERIES = {Univ. Lecture Ser.}, VOLUME = {46}, PUBLISHER = {Amer. Math. Soc.}, YEAR = {2008}, PAGES = {x+118}, ISBN = {978-0-8218-4727-5}, MRCLASS = {52C22 (37B50 52C23 55N05)}, MRNUMBER = {2446623 (2009m:52041)}, MRREVIEWER = {Bernd Sing}, } @book{GS:book, AUTHOR = {Gr\"{u}nbaum, Branko and Shephard, G C}, TITLE = {Tilings and Patterns}, YEAR = {1986}, ISBN = {0-716-71193-1}, PUBLISHER = {W. H. Freeman \& Co.}, ADDRESS = {New York, NY, USA}, } @article {BD, AUTHOR = {Barge, M. and Diamond, B.}, TITLE = {Cohomology in one-dimensional substitution tiling spaces}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {136}, YEAR = {2008}, PAGES = {2183--2191}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {37B05 (37A30 37B50 54H20)}, MRNUMBER = {2383524 (2009c:37005)}, MRREVIEWER = {Val{\'e}rie Berth{\'e}}, DOI = {10.1090/S0002-9939-08-09225-3}, URL = {http://dx.doi.org/10.1090/S0002-9939-08-09225-3}, } @article {H:rhomb, AUTHOR = {Harriss, E. O.}, TITLE = {Non-periodic rhomb substitution tilings that admit order {$n$} rotational symmetry}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {34}, YEAR = {2005}, PAGES = {523--536}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52C20}, MRNUMBER = {2160053 (2006e:52034)}, MRREVIEWER = {Peter M. Gruber}, DOI = {10.1007/s00454-005-1175-1}, URL = {http://dx.doi.org/10.1007/s00454-005-1175-1}, } @article {BDH:asymp-orbits, AUTHOR = {Barge, M. and Diamond, B. and Holton, C.}, TITLE = {Asymptotic orbits of primitive substitutions}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {301}, YEAR = {2003}, PAGES = {439--450}, ISSN = {0304-3975}, CODEN = {TCSDI}, MRCLASS = {68R15 (68Q45)}, MRNUMBER = {1975239 (2004d:68127)}, MRREVIEWER = {I. Mezn{\'{\i}}k}, DOI = {10.1016/S0304-3975(02)00889-7}, URL = {http://dx.doi.org/10.1016/S0304-3975(02)00889-7}, } @article {M:aperiodic, AUTHOR = {Moss{\'e}, B.}, TITLE = {Puissances de mots et reconnaissabilit\'e des points fixes d'une substitution}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {99}, YEAR = {1992}, PAGES = {327--334}, ISSN = {0304-3975}, CODEN = {TCSDI}, MRCLASS = {68R15}, MRNUMBER = {1168468 (93f:68076)}, MRREVIEWER = {Wit Fory{\'s}}, DOI = {10.1016/0304-3975(92)90357-L}, URL = {http://dx.doi.org/10.1016/0304-3975(92)90357-L}, } @article {S:aperiodic, AUTHOR = {Solomyak, B.}, TITLE = {Nonperiodicity implies unique composition for self-similar translationally finite tilings}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {20}, YEAR = {1998}, PAGES = {265--279}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52C22}, MRNUMBER = {1637896 (99f:52028)}, MRREVIEWER = {R. Blind}, DOI = {10.1007/PL00009386}, URL = {http://dx.doi.org/10.1007/PL00009386}, } @article {S:pisot, AUTHOR = {Solomyak, B.}, TITLE = {Dynamics of self-similar tilings}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {17}, YEAR = {1997}, PAGES = {695--738}, ISSN = {0143-3857}, MRCLASS = {52C22 (58F99)}, MRNUMBER = {1452190 (98f:52030)}, MRREVIEWER = {Mihail N. Kolountzakis}, DOI = {10.1017/S0143385797084988}, URL = {http://dx.doi.org/10.1017/S0143385797084988}, } @article {KSB:TTT, AUTHOR = {Klitzing, R. and Schlottmann, M. and Baake, M.}, TITLE = {Perfect matching rules for undecorated triangular tilings with {$10$}-, {$12$}-, and {$8$}-fold symmetry}, JOURNAL = {Internat. J. Modern Phys. B}, FJOURNAL = {International Journal of Modern Physics B. Condensed Matter Physics. Statistical Physics. Applied Physics}, VOLUME = {7}, YEAR = {1993}, PAGES = {1455--1473}, ISSN = {0217-9792}, MRCLASS = {52C20 (82D25)}, MRNUMBER = {1215344 (94d:52027)}, MRREVIEWER = {Hanna Nencka}, DOI = {10.1142/S0217979293002432}, URL = {http://dx.doi.org/10.1142/S0217979293002432}, } @article{GS:matching-rules, JSTOR_ARTICLETYPE = {research-article}, TITLE = {Matching Rules and Substitution Tilings}, AUTHOR = {Goodman-Strauss, C.}, JOURNAL = {Annals of Mathematics}, JSTOR_ISSUETITLE = {}, VOLUME = {147}, SERIES = {Second Series}, JSTOR_FORMATTEDDATE = {Jan., 1998}, PAGES = {pp. 181-223}, URL = {http://www.jstor.org/stable/120988}, ISSN = {0003486X}, ABSTRACT = {A substitution tiling is a certain globally defined hierarchical structure in a geometric space; we show that for any substitution tiling in Ed, d > 1, subject to relatively mild conditions, one can construct local rules that force the desired global structure to emerge. As an immediate corollary, infinite collections of forced aperiodic tilings are constructed. The theorem covers all known examples of hierarchical aperiodic tilings.}, LANGUAGE = {English}, YEAR = {1998}, PUBLISHER = {Annals of Mathematics}, COPYRIGHT = {Copyright © 1998 Annals of Mathematics}, } @article {BDHS:other, AUTHOR = {Barge, M. and Diamond, B. and Hunton, J. and Sadun, L.}, TITLE = {Cohomology of substitution tiling spaces}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {30}, YEAR = {2010}, PAGES = {1607--1627}, ISSN = {0143-3857}, MRCLASS = {37B50 (55N15)}, MRNUMBER = {2736888 (2011m:37018)}, MRREVIEWER = {Nicolas Bedaride}, DOI = {10.1017/S0143385709000777}, URL = {http://dx.doi.org/10.1017/S0143385709000777}, } @article{FH:worms, AUTHOR = {Frettl{\"o}h, Dirk and Harriss, Edmund}, TITLE = {Parallelogram tilings, worms, and finite orientations}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {49}, YEAR = {2013}, PAGES = {531--539}, ISSN = {0179-5376}, CODEN = {DCGEER}, MRCLASS = {52C23}, MRNUMBER = {3038528}, MRREVIEWER = {Elizaveta Zamorzaeva}, DOI = {10.1007/s00454-012-9478-5}, URL = {http://dx.doi.org/10.1007/s00454-012-9478-5}, } @misc{TE, AUTHOR = {Frettl\"{o}h, D. and Harriss, E. O.}, TITLE = {The Tilings Encyclopedia}, URL = {http://tilings.math.uni-bielefeld.de/}, NOTE = {Accessed: 2014-08-29} } @article{RW:cool-lex, AUTHOR = {Ruskey, Frank and Williams, Aaron}, TITLE = {The coolest way to generate combinations}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {309}, YEAR = {2009}, PAGES = {5305--5320}, ISSN = {0012-365X}, CODEN = {DSMHA4}, MRCLASS = {05A05}, MRNUMBER = {2548545 (2010k:05016)}, DOI = {10.1016/j.disc.2007.11.048}, URL = {http://dx.doi.org/10.1016/j.disc.2007.11.048}, } @inproceedings{W:multisets, author = {Williams, Aaron}, title = {Loopless Generation of Multiset Permutations Using a Constant Number of Variables by Prefix Shifts}, booktitle = {Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms}, series = {SODA '09}, year = {2009}, location = {New York, New York}, pages = {987--996}, numpages = {10}, url = {http://dl.acm.org/citation.cfm?id=1496770.1496877}, acmid = {1496877}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, } % RANDOM SUBSTITUTIONS @article {GL:random, AUTHOR = {Godr{\`e}che, C. and Luck, J. M.}, TITLE = {Quasiperiodicity and randomness in tilings of the plane}, JOURNAL = {J. Statist. Phys.}, FJOURNAL = {Journal of Statistical Physics}, VOLUME = {55}, YEAR = {1989}, PAGES = {1--28}, ISSN = {0022-4715}, CODEN = {JSTPSB}, MRCLASS = {52C20 (82D25)}, MRNUMBER = {1003500 (91c:52025)}, MRREVIEWER = {Eugen Belokolos}, DOI = {10.1007/BF01042590}, URL = {http://dx.doi.org/10.1007/BF01042590}, } @article {N:random-one, AUTHOR = {Nilsson, J.}, TITLE = {On the entropy of a family of random substitutions}, JOURNAL = {Monatsh. Math.}, FJOURNAL = {Monatshefte f\"ur Mathematik}, VOLUME = {168}, YEAR = {2012}, PAGES = {563--577}, ISSN = {0026-9255}, MRCLASS = {37Bxx (68R15)}, MRNUMBER = {2993964}, DOI = {10.1007/s00605-012-0401-1}, URL = {http://dx.doi.org/10.1007/s00605-012-0401-1}, } @article {N:random-two, AUTHOR = {Nilsson, J.}, TITLE = {On the entropy of a two step random {F}ibonacci substitution}, JOURNAL = {Entropy}, FJOURNAL = {Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies}, VOLUME = {15}, YEAR = {2013}, PAGES = {3312--3324}, ISSN = {1099-4300}, MRCLASS = {68R15 (05A16)}, MRNUMBER = {3111435}, DOI = {10.3390/e15093312}, URL = {http://dx.doi.org/10.3390/e15093312}, } @incollection{BM:noble-means, YEAR = {2013}, ISBN = {978-94-007-6430-9}, BOOKTITLE = {Aperiodic Crystals}, EDITOR = {Schmid, Siegbert and Withers, Ray L. and Lifshitz, Ron}, DOI = {10.1007/978-94-007-6431-6_3}, TITLE = {Random Noble Means Substitutions}, URL = {http://dx.doi.org/10.1007/978-94-007-6431-6_3}, PUBLISHER = {Springer Netherlands}, AUTHOR = {Baake, M. and Moll, M.}, PAGES = {19-27}, LANGUAGE = {English} } % MULTI-SUBSTITUTIONS @article {GM:multi-one-d, AUTHOR = {G{\"a}hler, F. and Maloney, G. R.}, TITLE = {Cohomology of one-dimensional mixed substitution tiling spaces}, JOURNAL = {Topology Appl.}, FJOURNAL = {Topology and its Applications}, VOLUME = {160}, YEAR = {2013}, PAGES = {703--719}, ISSN = {0166-8641}, CODEN = {TIAPD9}, MRCLASS = {55N05 (37B10 37B50 52C23 54H20)}, MRNUMBER = {3022738}, MRREVIEWER = {Vladimer L. Baladze}, DOI = {10.1016/j.topol.2013.01.019}, URL = {http://dx.doi.org/10.1016/j.topol.2013.01.019}, } @article {PV:frequency, AUTHOR = {Pacheco, R. and Vilarinho, H.}, TITLE = {Statistical stability for multi-substitution tiling spaces}, JOURNAL = {Discrete Contin. Dyn. Syst.}, FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A}, VOLUME = {33}, YEAR = {2013}, PAGES = {4579--4594}, ISSN = {1078-0947}, MRCLASS = {37A25 (37A15 52C22)}, MRNUMBER = {3049092}, MRREVIEWER = {Douglas P. Dokken}, DOI = {10.3934/dcds.2013.33.4579}, URL = {http://dx.doi.org/10.3934/dcds.2013.33.4579}, } @article {PFS:fusion, YEAR = {2013}, ISSN = {0046-5755}, JOURNAL = {Geometriae Dedicata}, DOI = {10.1007/s10711-013-9893-7}, TITLE = {Fusion: a general framework for hierarchical tilings of $\mathbb{R }^d$}, URL = {http://dx.doi.org/10.1007/s10711-013-9893-7}, PUBLISHER = {Springer Netherlands}, KEYWORDS = {Self-similar; Substitution; Mixing; Dynamical spectrum; Invariant measures; Primary: 37B50; Secondary: 52C23; 37A25; 37B10}, AUTHOR = {Frank, NataliePriebe and Sadun, Lorenzo}, PAGES = {1-38}, LANGUAGE = {English} } @article{D:lin-recurrent, AUTHOR = {Durand,F.}, TITLE = {Linearly recurrent subshifts have a finite number of non-periodic subshift factors}, JOURNAL = {Ergodic Theory Dynam. Systems}, VOLUME = {20}, ISSUE = {04}, MONTH = {8}, YEAR = {2000}, ISSN = {1469-4417}, PAGES = {1061--1078}, NUMPAGES = {18}, DOI = {null}, URL = {http://journals.cambridge.org/article_S0143385700000584}, } @article{D:derived-seqs, AUTHOR = {Durand, F.}, TITLE = {A characterization of substitutive sequences using return words}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {179}, YEAR = {1998}, PAGES = {89--101}, ISSN = {0012-365X}, CODEN = {DSMHA4}, MRCLASS = {68R15 (68Q68)}, MRNUMBER = {1489074 (99g:68157)}, MRREVIEWER = {Val{\'e}rie Berth{\'e}}, DOI = {10.1016/S0012-365X(97)00029-0}, URL = {http://dx.doi.org/10.1016/S0012-365X(97)00029-0}, } @article {R:rauzy-fractals, AUTHOR = {Rauzy, G.}, TITLE = {Nombres alg\'ebriques et substitutions}, JOURNAL = {Bull. Soc. Math. France}, FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France}, VOLUME = {110}, YEAR = {1982}, PAGES = {147--178}, ISSN = {0037-9484}, CODEN = {BSMFAA}, MRCLASS = {10K99 (10F25)}, MRNUMBER = {667748 (84h:10074)}, MRREVIEWER = {A. D. Pollington}, URL = {http://www.numdam.org/item?id=BSMF_1982__110__147_0}, } @article {P:thue-morse, AUTHOR = {Prouhet, E.}, TITLE = {M\'emoir sur quelques relations entre les puissances des nombres}, JOURNAL = {C. R. Math. Acad. Sci. Paris}, VOLUME = {1}, YEAR = {1851}, PAGES = {225}, } @article{F:s-adic, AUTHOR = {Ferenczi,S.}, TITLE = {Rank and symbolic complexity}, JOURNAL = {Ergodic Theory Dynam. Systems}, VOLUME = {16}, ISSUE = {04}, MONTH = {8}, YEAR = {1996}, ISSN = {1469-4417}, PAGES = {663--682}, NUMPAGES = {20}, DOI = {10.1017/S0143385700009032}, URL = {http://journals.cambridge.org/article_S0143385700009032}, } @article{WW:projection, AUTHOR = {Whittaker, E. J. W. and Whittaker, R. M.}, TITLE = {Some generalized {P}enrose patterns from projections of {$n$}-dimensional lattices}, JOURNAL = {Acta Cryst. Sect. A}, FJOURNAL = {Acta Crystallographica. Section A. Crystal Physics, Diffraction, Theoretical and General Crystallography}, VOLUME = {44}, YEAR = {1988}, PAGES = {105--112}, ISSN = {0108-7673}, CODEN = {ACACEQ}, MRCLASS = {52A45 (05B45)}, MRNUMBER = {932292 (89f:52042)}, MRREVIEWER = {Marjorie Senechal}, DOI = {10.1107/S0108767387009279}, URL = {http://dx.doi.org/10.1107/S0108767387009279}, } @article {DL:linearly-recurrent, AUTHOR = {Damanik, D. and Lenz, D.}, TITLE = {Substitution dynamical systems: characterization of linear repetitivity and applications}, JOURNAL = {J. Math. Anal. Appl.}, FJOURNAL = {Journal of Mathematical Analysis and Applications}, VOLUME = {321}, YEAR = {2006}, PAGES = {766--780}, ISSN = {0022-247X}, CODEN = {JMANAK}, MRCLASS = {37B10 (37A20 37A25 39A70 47B36 47B80 81Q10 82D25)}, MRNUMBER = {2241154 (2007d:37008)}, MRREVIEWER = {C{\'e}sar R. de Oliveira}, DOI = {10.1016/j.jmaa.2005.09.004}, URL = {http://dx.doi.org/10.1016/j.jmaa.2005.09.004}, } @article {B:undecidability, AUTHOR = {Berger, R.}, TITLE = {The undecidability of the domino problem}, JOURNAL = {Mem. Amer. Math. Soc.}, FJOURNAL = {Memoirs of the American Mathematical Society}, VOLUME = {66}, YEAR = {1966}, PAGES = {1--72}, ISSN = {0065-9266}, MRCLASS = {02.74}, MRNUMBER = {0216954}, MRREVIEWER = {J. R. B{\"u}chi}, } @book{B:bott-tu, title={Differential Forms in Algebraic Topology}, author={Bott, R. and Tu, L. W.}, isbn={9781475739510}, series={Grad. 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Paris}, FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, VOLUME = {350}, YEAR = {2012}, PAGES = {979--983}, ISSN = {1631-073X}, MRCLASS = {37B10}, MRNUMBER = {2996779}, DOI = {10.1016/j.crma.2012.10.015}, URL = {http://dx.doi.org/10.1016/j.crma.2012.10.015}, } @article{BD:pisot-coincidence, AUTHOR = {Barge, M. and Diamond, B.}, TITLE = {Coincidence for substitutions of {P}isot type}, JOURNAL = {Bull. Soc. Math. France}, VOLUME = {130}, YEAR = {2002}, PAGES = {619--626} } @article{B:pisot-beta-subs, AUTHOR = {{Barge}, M.}, TITLE = {The {P}isot conjecture for $\beta$-substitutions}, JOURNAL = {to appear in Ergodic Theory Dynam. Systems}, YEAR = {2017}, PAGES = {}, DOI = {10.1017/etds.2016.44}, NOTES = {Published online DOI:10.1017/etds.2016.44}, } @article {J:complexity, AUTHOR = {Julien, A.}, TITLE = {Complexity and cohomology for cut-and-projection tilings}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {30}, YEAR = {2010}, PAGES = {489--523}, ISSN = {0143-3857}, MRCLASS = {52C45 (05B45 37B50 52C23)}, MRNUMBER = {2599890}, MRREVIEWER = {Bernd Sing}, DOI = {10.1017/S0143385709000194}, URL = {http://dx.doi.org/10.1017/S0143385709000194}, } @article{HL:periodicity, AUTHOR = {Harju, T. and Linna, M.}, TITLE = {On the periodicity of morphisms on free monoids}, JOURNAL = {RAIRO Theor. Inform. Appl.}, VOLUME = {20}, YEAR = {1986}, PAGES = {47--54} } @inproceedings{ER:iterates-of-words, AUTHOR = {Ehrenfeucht, A. and Rozenberg, G.}, TITLE = {On simplifications of {PDOL} systems}, BOOKTITLE = {Proceedings of a {C}onference on {T}heoretical {C}omputer {S}cience ({U}niv. {W}aterloo, {W}aterloo, {O}nt., 1977)}, PAGES = {81--87}, PUBLISHER = {Comput. Sci. Dept., Univ. Waterloo, Waterloo, Ont.}, YEAR = {1978}, MRCLASS = {68A30}, MRNUMBER = {0495235 (58 \#13962)}, MRREVIEWER = {K. P. 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Math.}, FJOURNAL = {New York Journal of Mathematics}, VOLUME = {18}, YEAR = {2012}, PAGES = {765--796}, ISSN = {1076-9803}, MRCLASS = {37B25 (52C22 55P55)}, MRNUMBER = {2991423}, URL = {http://nyjm.albany.edu:8000/j/2012/18_765.html} } @book{L:comp-sci-book, title={Wang Tiles in Computer Graphics}, author={Lagae, A.}, isbn={9781598299663}, series={Synthesis Lectures on Computer Graphics and Animation}, url={https://books.google.co.uk/books?id=SYRfAQAAQBAJ}, year={2009}, publisher={Morgan \& Claypool Publishers} } @incollection {BHZ:gap-labeling, AUTHOR = {Bellissard, J. and Herrmann, D. J. L. and Zarrouati, M.}, TITLE = {Hulls of aperiodic solids and gap labeling theorems}, BOOKTITLE = {Directions in Mathematical Quasicrystals}, SERIES = {CRM Monogr. Ser.}, VOLUME = {13}, PAGES = {207--258}, PUBLISHER = {Amer. Math. Soc.}, YEAR = {2000}, MRCLASS = {82D20 (19K14 52C23 81R60 82D25)}, MRNUMBER = {1798994 (2002a:82101)}, MRREVIEWER = {Johannes Kellendonk}, } @article{T:virology-tilings, title = "A tiling approach to virus capsid assembly explaining a structural puzzle in virology ", journal = "J. Theoret. Biol. ", volume = "226", pages = "477--482", year = "2004", note = "", issn = "0022-5193", doi = "http://dx.doi.org/10.1016/j.jtbi.2003.10.006", url = "http://www.sciencedirect.com/science/article/pii/S0022519303003928", author = "R. Twarock", keywords = "Caspar?Klug theory", keywords = "Viral capsids", keywords = "Polyoma virus", keywords = "L-A virus ", abstract = "A novel approach for the description of the protein stoichiometry of viral capsids, that is the protein shells protecting the viral genome, is introduced based on tiling theory. This approach generalizes Caspar?Klug theory of quasi-equivalence to account also for non-quasi-equivalent subunit arrangements in icosahedral virus capsids that have been observed experimentally but are not covered by the Caspar?Klug approach. In particular, the new approach is used to explain the structure of polyoma virus, Simian Virus 40 and L-A virus capsids, which are considered structural puzzles in view of Caspar?Klug theory. " } @article {BS:beta-numerations, AUTHOR = {Berth{\'e}, V. and Siegel, A.}, TITLE = {Tilings associated with beta-numeration and substitutions}, JOURNAL = {Integers}, FJOURNAL = {Integers. 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Series A}, VOLUME = {33}, YEAR = {2013}, PAGES = {579--597}, ISSN = {1078-0947}, MRCLASS = {37B50 (37B05)}, MRNUMBER = {2975125}, DOI = {10.3934/dcds.2013.33.579}, URL = {http://dx.doi.org/10.3934/dcds.2013.33.579}, } @incollection {ABBL:pisot, AUTHOR = {Akiyama, S. and Barge, M. and Berth{\'e}, V. and Lee, J.-Y. and Siegel, A.}, TITLE = {On the {P}isot substitution conjecture}, BOOKTITLE = {Mathematics of Aperiodic Order}, SERIES = {Progr. Math.}, VOLUME = {309}, PAGES = {33--72}, PUBLISHER = {Birkh\"auser/Springer}, YEAR = {2015}, MRCLASS = {37B50 (11K16 37B05 37B10)}, MRNUMBER = {3381478}, DOI = {10.1007/978-3-0348-0903-0_2}, URL = {http://dx.doi.org/10.1007/978-3-0348-0903-0_2}, } @article {BJS:arnoux-rauzy, AUTHOR = {Berth{\'e}, V. and Jolivet, T. and Siegel, A.}, TITLE = {Substitutive {A}rnoux-{R}auzy sequences have pure discrete spectrum}, JOURNAL = {Unif. Distrib. Theory}, FJOURNAL = {Uniform Distribution Theory}, VOLUME = {7}, YEAR = {2012}, PAGES = {173--197}, ISSN = {1336-913X}, MRCLASS = {37B10 (37A30)}, MRNUMBER = {2943167}, MRREVIEWER = {Paul Surer}, } @article {CS:shape, AUTHOR = {Clark, A. and Sadun, L.}, TITLE = {When shape matters: deformations of tiling spaces}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {26}, YEAR = {2006}, PAGES = {69--86}, ISSN = {0143-3857}, MRCLASS = {37B50 (52C23)}, MRNUMBER = {2201938}, MRREVIEWER = {Natalie Priebe Frank}, DOI = {10.1017/S0143385705000623}, URL = {http://dx.doi.org/10.1017/S0143385705000623}, } @article {HS:pisot, AUTHOR = {Hollander, M. and Solomyak, B.}, TITLE = {Two-symbol {P}isot substitutions have pure discrete spectrum}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {23}, YEAR = {2003}, PAGES = {533--540}, ISSN = {0143-3857}, MRCLASS = {37A30 (37A35)}, MRNUMBER = {1972237}, MRREVIEWER = {Ali Messaoudi}, DOI = {10.1017/S0143385702001384}, URL = {http://dx.doi.org/10.1017/S0143385702001384}, } @article {B:proper-bijective, AUTHOR = {Barge, M.}, TITLE = {Pure discrete spectrum for a class of one-dimensional substitution tiling systems}, JOURNAL = {Discrete Contin. Dyn. Syst.}, FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A}, VOLUME = {36}, YEAR = {2016}, PAGES = {1159--1173}, ISSN = {1078-0947}, MRCLASS = {37B50 (11A55)}, MRNUMBER = {3431249}, DOI = {10.3934/dcds.2016.36.1159}, URL = {http://dx.doi.org/10.3934/dcds.2016.36.1159}, } @article {AGL:pisot, AUTHOR = {Akiyama, S. and G{\"a}hler, F. and Lee, J.-Y.}, TITLE = {Determining pure discrete spectrum for some self-affine tilings}, JOURNAL = {Discrete Math. Theor. Comput. 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Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {336}, YEAR = {1993}, PAGES = {121--149}, ISSN = {0002-9947}, MRCLASS = {58F03 (28D20 46L99 54H20)}, MRNUMBER = {1102219}, MRREVIEWER = {Fred W. Roush}, DOI = {10.2307/2154341}, URL = {http://dx.doi.org/10.2307/2154341}, } @article {D:decomposable, AUTHOR = {Dugas, M.}, TITLE = {Torsion-free abelian groups defined by an integral matrix}, JOURNAL = {Int. J. Algebra}, FJOURNAL = {International Journal of Algebra}, VOLUME = {6}, YEAR = {2012}, PAGES = {85--99}, ISSN = {1312-8868}, MRCLASS = {20K15 (15B36)}, MRNUMBER = {2876158}, MRREVIEWER = {Frank Okoh}, } @article {BGG:substitutions, AUTHOR = {Baake, M. and G{\"a}hler, F. and Grimm, U.}, TITLE = {Examples of substitution systems and their factors}, JOURNAL = {J. Integer Seq.}, FJOURNAL = {Journal of Integer Sequences}, VOLUME = {16}, YEAR = {2013}, PAGES = {Article 13.2.14, 18}, ISSN = {1530-7638}, MRCLASS = {37B10 (52C22)}, MRNUMBER = {3032397}, MRREVIEWER = {Karsten Keller}, } @incollection {R:rauzy-graphs, AUTHOR = {Rauzy, G.}, TITLE = {Suites \`a termes dans un alphabet fini}, BOOKTITLE = {Seminar on Number Theory, 1982--1983 ({T}alence, 1982/1983)}, PAGES = {Exp. No. 25, 16}, PUBLISHER = {Univ. Bordeaux I, Talence}, YEAR = {1983}, MRCLASS = {11K31 (05A99 54H20)}, MRNUMBER = {750326}, MRREVIEWER = {Pierre Michel}, } @misc {R:stack-exchange, TITLE = {How to test if a primitive matrix has an eigenvalue of unit modulus, \url{http://math.stackexchange.com/q/1440992}}, AUTHOR = {Bourgeois, G.}, HOWPUBLISHED = {Math. Stack Exchange}, YEAR = {2015}, } @article {T:thue-morse, AUTHOR = {Thue, A.}, TITLE = {\"{U}ber unendliche {Z}eichenreihen}, JOURNAL = {Norske vid. Selsk. Skr. Mat. Nat. 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