{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T15:37:32Z","timestamp":1649086652928},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2011,4,20]],"date-time":"2011-04-20T00:00:00Z","timestamp":1303257600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2011,9]]},"DOI":"10.1007\/s00454-011-9349-5","type":"journal-article","created":{"date-parts":[[2011,4,19]],"date-time":"2011-04-19T17:03:06Z","timestamp":1303232586000},"page":"223-251","source":"Crossref","is-referenced-by-count":2,"title":["Rigidity of Quasicrystallic and Z \u03b3 -Circle Patterns"],"prefix":"10.1007","volume":"46","author":[{"given":"Ulrike","family":"B\u00fccking","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,4,20]]},"reference":[{"key":"9349_CR1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s00454-002-0761-8","volume":"29","author":"S.I. Agafonov","year":"2003","unstructured":"Agafonov, S.I.: Imbedded circle patterns with the combinatorics of the square grid and discrete Painlev\u00e9 equations. Discrete Comput. Geom. 29, 305\u2013319 (2003)","journal-title":"Discrete Comput. Geom."},{"key":"9349_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2991\/jnmp.2005.12.s2.1","volume":"12","author":"S.I. Agafonov","year":"2005","unstructured":"Agafonov, S.I.: Asymptotic behavior of discrete holomorphic maps z c , log\u2009(z). J. Nonlinear Math. Phys. 12, 1\u201314 (2005)","journal-title":"J. Nonlinear Math. Phys."},{"key":"9349_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0017089505002247","volume":"47","author":"S.I. Agafonov","year":"2005","unstructured":"Agafonov, S.I.: Discrete Riccati equation, hypergeometric functions and circle patterns of Schramm type. Glasg. Math. J. A 47, 1\u201316 (2005)","journal-title":"Glasg. Math. J. A"},{"key":"9349_CR4","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1155\/S1073792800000118","volume":"4","author":"S.I. Agafonov","year":"2000","unstructured":"Agafonov, S.I., Bobenko, A.I.: Discrete Z \u03b3 and Painlev\u00e9 equations. Int. Math. Res. Not. 4, 165\u2013193 (2000)","journal-title":"Int. Math. Res. Not."},{"key":"9349_CR5","doi-asserted-by":"crossref","first-page":"247","DOI":"10.4153\/CMB-1990-039-5","volume":"33","author":"D. Aharonov","year":"1990","unstructured":"Aharonov, D.: The hexagonal packing lemma and discrete potential theory. Can. Math. Bull. 33, 247\u2013252 (1990)","journal-title":"Can. Math. Bull."},{"key":"9349_CR6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.2307\/2154526","volume":"343","author":"D. Aharonov","year":"1994","unstructured":"Aharonov, D.: The hexagonal packing lemma and the Rodin Sullivan conjecture. Trans. Am. Math. Soc. 343, 157\u2013167 (1994)","journal-title":"Trans. Am. Math. Soc."},{"key":"9349_CR7","series-title":"London Mathematical Society Lecture Notes Series","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1017\/CBO9780511569432.009","volume-title":"Symmetries and Integrability of Difference Equations","author":"A.I. Bobenko","year":"1999","unstructured":"Bobenko, A.I.: Discrete conformal maps and surfaces. In: Clarkson, P.A., Nijhoff, F.W. (eds.) Symmetries and Integrability of Difference Equations. London Mathematical Society Lecture Notes Series, vol. 255, pp. 97\u2013108. Cambridge University Press, Cambridge (1999)"},{"key":"9349_CR8","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1215\/S0012-7094-03-11635-X","volume":"116","author":"A.I. Bobenko","year":"2003","unstructured":"Bobenko, A.I., Hoffmann, T.: Hexagonal circle patterns and integrable systems: patterns with constant angles. Duke Math. J. 116, 525\u2013566 (2003)","journal-title":"Duke Math. J."},{"key":"9349_CR9","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1090\/S0002-9947-03-03239-2","volume":"356","author":"A.I. Bobenko","year":"2004","unstructured":"Bobenko, A.I., Springborn, B.A.: Variational principles for circle patterns and Koebe\u2019s theorem. Trans. Am. Math. Soc. 356, 659\u2013689 (2004)","journal-title":"Trans. Am. Math. Soc."},{"key":"9349_CR10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1515\/crll.2005.2005.583.117","volume":"583","author":"A.I. Bobenko","year":"2005","unstructured":"Bobenko, A.I., Mercat, Ch., Suris, Yu.B.: Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green\u2019s function. J. Reine Angew. Math. 583, 117\u2013161 (2005)","journal-title":"J. Reine Angew. Math."},{"key":"9349_CR11","series-title":"Graduate Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7643-8621-4","volume-title":"Discrete Differential Geometry. Integrable Structure","author":"A.I. Bobenko","year":"2008","unstructured":"Bobenko, A.I., Suris, Yu.B.: Discrete Differential Geometry. Integrable Structure. Graduate Studies in Mathematics, vol.\u00a098. AMS, Providence (2008)"},{"key":"9349_CR12","unstructured":"B\u00fccking, U.: Approximation of conformal mappings by circle patterns and discrete minimal surfaces. Ph.D. thesis, Technische Universit\u00e4t Berlin (2007). Published online at http:\/\/opus.kobv.de\/tuberlin\/volltexte\/2008\/1764\/"},{"key":"9349_CR13","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10711-008-9292-7","volume":"137","author":"U. B\u00fccking","year":"2008","unstructured":"B\u00fccking, U.: Approximation of conformal mapping by circle patterns. Geom. Dedic. 137, 163\u2013197 (2008)","journal-title":"Geom. Dedic."},{"key":"9349_CR14","series-title":"Carus Mathematics Monographs","doi-asserted-by":"crossref","DOI":"10.5948\/UPO9781614440222","volume-title":"Random Walks and Electric Networks","author":"P.G. Doyle","year":"1984","unstructured":"Doyle, P.G., Snell, J.L.: Random Walks and Electric Networks. Carus Mathematics Monographs, vol.\u00a022. Math. Assoc. Am., Washington (1984)"},{"key":"9349_CR15","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1017\/S0305004196001557","volume":"121","author":"T. Dubejko","year":"1997","unstructured":"Dubejko, T.: Recurrent random walks, Liouville\u2019s theorem, and circle packings. Math. Proc. Camb. Philos. Soc. 121, 531\u2013546 (1997)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"9349_CR16","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1103\/PhysRevLett.54.2688","volume":"54","author":"M. Duneau","year":"1985","unstructured":"Duneau, M., Katz, A.: Quasiperiodic patterns. Phys. Rev. Lett. 54, 2688\u20132691 (1985)","journal-title":"Phys. Rev. Lett."},{"key":"9349_CR17","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1088\/0305-4470\/19\/2\/020","volume":"19","author":"F. G\u00e4hler","year":"1986","unstructured":"G\u00e4hler, F., Rhyner, J.: Equivalence of the generalized grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A 19, 267\u2013277 (1986)","journal-title":"J. Phys. A"},{"key":"9349_CR18","doi-asserted-by":"crossref","first-page":"395","DOI":"10.4310\/jdg\/1214446324","volume":"33","author":"Z.-X. He","year":"1991","unstructured":"He, Z.-X.: An estimate for hexagonal circle packings. J. Differ. Geom. 33, 395\u2013412 (1991)","journal-title":"J. Differ. Geom."},{"key":"9349_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/121018","volume":"149","author":"Z.-X. He","year":"1999","unstructured":"He, Z.-X.: Rigidity of infinite disk patterns. Ann. Math. 149, 1\u201333 (1999)","journal-title":"Ann. Math."},{"key":"9349_CR20","first-page":"369","volume":"137","author":"Z.-X. He","year":"1993","unstructured":"He, Z.-X., Schramm, O.: Fixed points, Koebe uniformization and circle packings. J. Am. Math. Soc. 137, 369\u2013406 (1993)","journal-title":"J. Am. Math. Soc."},{"key":"9349_CR21","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1145\/1138450.1138461","volume":"25","author":"L. Kharevych","year":"2006","unstructured":"Kharevych, L., Springborn, B., Schr\u00f6der, P.: Discrete conformal mappings via circle patterns. ACM Trans. Graph. 25, 412\u2013438 (2006)","journal-title":"ACM Trans. Graph."},{"key":"9349_CR22","doi-asserted-by":"crossref","first-page":"349","DOI":"10.4310\/jdg\/1214441375","volume":"26","author":"B. Rodin","year":"1987","unstructured":"Rodin, B., Sullivan, D.: The convergence of circle packings to the Riemann mapping. J. Differ. Geom. 26, 349\u2013360 (1987)","journal-title":"J. Differ. Geom."},{"key":"9349_CR23","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1090\/S0894-0347-1991-1076089-9","volume":"4","author":"O. Schramm","year":"1991","unstructured":"Schramm, O.: Rigidity of infinite (circle) packings. J. Am. Math. Soc. 4, 127\u2013149 (1991)","journal-title":"J. Am. Math. Soc."},{"key":"9349_CR24","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1215\/S0012-7094-97-08611-7","volume":"86","author":"O. Schramm","year":"1997","unstructured":"Schramm, O.: Circle patterns with the combinatorics of the square grid. Duke Math. J. 86, 347\u2013389 (1997)","journal-title":"Duke Math. J."},{"key":"9349_CR25","unstructured":"Schreiber, V.: Quasicrystallic circle patterns, the discrete power function. Diplomarbeit (2008). Technische Universit\u00e4t Berlin"},{"key":"9349_CR26","volume-title":"Quasicrystals and Geometry","author":"M. Senechal","year":"1995","unstructured":"Senechal, M.: Quasicrystals and Geometry. Cambridge University Press, Cambridge (1995)"},{"key":"9349_CR27","unstructured":"Springborn, B.A.: Variational principles for circle patterns. Ph.D. thesis, Technische Universit\u00e4t Berlin (2003). Published online at http:\/\/opus.kobv.de\/tuberlin\/volltexte\/2003\/668\/"},{"key":"9349_CR28","volume-title":"Introduction to Circle Packing: The Theory of Discrete Analytic Functions","author":"K. Stephenson","year":"2005","unstructured":"Stephenson, K.: Introduction to Circle Packing: The Theory of Discrete Analytic Functions. Cambridge University Press, New York (2005)"},{"key":"9349_CR29","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511470967","volume-title":"Random Walks on Infinite Graphs and Groups","author":"W. Woess","year":"2000","unstructured":"Woess, W.: Random Walks on Infinite Graphs and Groups. Cambridge University Press, Cambridge (2000)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-011-9349-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-011-9349-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-011-9349-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T11:20:20Z","timestamp":1592479220000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-011-9349-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,20]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["9349"],"URL":"https:\/\/doi.org\/10.1007\/s00454-011-9349-5","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,4,20]]}}}