{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T20:23:12Z","timestamp":1694636592262},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2009,7,17]],"date-time":"2009-07-17T00:00:00Z","timestamp":1247788800000},"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":[[2009,12]]},"DOI":"10.1007\/s00454-009-9213-z","type":"journal-article","created":{"date-parts":[[2009,7,16]],"date-time":"2009-07-16T19:14:42Z","timestamp":1247771682000},"page":"740-758","source":"Crossref","is-referenced-by-count":1,"title":["Uniqueness in Discrete Tomography of Delone Sets with\u00a0Long-Range Order"],"prefix":"10.1007","volume":"42","author":[{"given":"Christian","family":"Huck","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,7,17]]},"reference":[{"key":"9213_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02293033","volume":"8","author":"R. Ammann","year":"1992","unstructured":"Ammann, R., Gr\u00fcnbaum, B., Shephard, G.C.: Aperiodic tiles. Discrete Comput. Geom. 8, 1\u201325 (1992)","journal-title":"Discrete Comput. Geom."},{"key":"9213_CR2","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1080\/14786430601083330","volume":"87","author":"M. Baake","year":"2007","unstructured":"Baake, M., Huck, C.: Discrete tomography of Penrose model sets. Philos. Mag. 87, 2839\u20132846 (2007). arXiv:math-ph\/0610056v1","journal-title":"Philos. Mag."},{"key":"9213_CR3","doi-asserted-by":"crossref","first-page":"8091","DOI":"10.1103\/PhysRevB.42.8091","volume":"42","author":"M. Baake","year":"1990","unstructured":"Baake, M., Joseph, D.: Ideal and defective vertex configurations in the planar octagonal quasilattice. Phys. Rev. B 42, 8091\u20138102 (1990)","journal-title":"Phys. Rev. B"},{"key":"9213_CR4","series-title":"CRM Monograph Series","volume-title":"Directions in Mathematical Quasicrystals","year":"2000","unstructured":"Baake, M., Moody, R.V. (eds.): Directions in Mathematical Quasicrystals. CRM Monograph Series, vol.\u00a013. AMS, Providence (2000)"},{"key":"9213_CR5","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1142\/S0217984990000313","volume":"4","author":"M. Baake","year":"1990","unstructured":"Baake, M., Kramer, P., Schlottmann, M., Zeidler, D.: The triangle pattern\u2014a new quasiperiodic tiling with fivefold symmetry. Mod. Phys. Lett. B 4, 249\u2013258 (1990)","journal-title":"Mod. Phys. Lett. B"},{"key":"9213_CR6","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1142\/S0217979290001054","volume":"4","author":"M. Baake","year":"1990","unstructured":"Baake, M., Kramer, P., Schlottmann, M., Zeidler, D.: Planar patterns with fivefold symmetry as sections of periodic structures in 4-space. Int. J. Mod. Phys. B 4, 2217\u20132268 (1990)","journal-title":"Int. J. Mod. Phys. B"},{"key":"9213_CR7","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1107\/S0108767306030091","volume":"62","author":"M. Baake","year":"2006","unstructured":"Baake, M., Gritzmann, P., Huck, C., Langfeld, B., Lord, K.: Discrete tomography of planar model sets. Acta Crystallogr. A 62, 419\u2013433 (2006). arXiv:math\/0609393v1 [math.MG]","journal-title":"Acta Crystallogr. A"},{"key":"9213_CR8","volume-title":"Number Theory","author":"Z.I. Borevich","year":"1966","unstructured":"Borevich, Z.I., Shafarevich, I.R.: Number Theory. Academic Press, San Diego (1966)"},{"key":"9213_CR9","first-page":"298","volume":"2","author":"M.G. Darboux","year":"1878","unstructured":"Darboux, M.G.: Sur un probl\u00e8me de g\u00e9om\u00e9trie \u00e9l\u00e9mentaire. Bull. Sci. Math. 2, 298\u2013304 (1878)","journal-title":"Bull. Sci. Math."},{"key":"9213_CR10","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/0022-3093(93)90335-U","volume":"153\u2013154","author":"F. G\u00e4hler","year":"1993","unstructured":"G\u00e4hler, F.: Matching rules for quasicrystals: the composition\u2013decomposition method. J. Non-Cryst. Solids 153\u2013154, 160\u2013164 (1993)","journal-title":"J. Non-Cryst. Solids"},{"key":"9213_CR11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107341029","volume-title":"Geometric Tomography","author":"R.J. Gardner","year":"2006","unstructured":"Gardner, R.J.: Geometric Tomography, 2nd edn. Cambridge University Press, Cambridge (2006)","edition":"2"},{"key":"9213_CR12","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1090\/S0002-9947-97-01741-8","volume":"349","author":"R.J. Gardner","year":"1997","unstructured":"Gardner, R.J., Gritzmann, P.: Discrete tomography: determination of finite sets by X-rays. Trans. Am. Math. Soc. 349, 2271\u20132295 (1997)","journal-title":"Trans. Am. Math. Soc."},{"key":"9213_CR13","doi-asserted-by":"crossref","unstructured":"Gardner, R.J., Gritzmann, P.: Uniqueness and complexity in discrete tomography. In: [19], pp. 85\u2013114","DOI":"10.1007\/978-1-4612-1568-4_4"},{"key":"9213_CR14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0012-365X(98)00347-1","volume":"202","author":"R.J. Gardner","year":"1999","unstructured":"Gardner, R.J., Gritzmann, P., Prangenberg, D.: On the computational complexity of reconstructing lattice sets from their X-rays. Discrete Math. 202, 45\u201371 (1999)","journal-title":"Discrete Math."},{"key":"9213_CR15","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1112\/jlms\/s2-21.1.171","volume":"21","author":"R.J. Gardner","year":"1980","unstructured":"Gardner, R.J., McMullen, P.: On Hammer\u2019s X-ray problem. J. Lond. Math. Soc. (2) 21, 171\u2013175 (1980)","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"9213_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-22278-2","volume-title":"p-adic Numbers","author":"F.Q. Gouv\u00eaa","year":"1993","unstructured":"Gouv\u00eaa, F.Q.: p-adic Numbers. Springer, New York (1993)"},{"key":"9213_CR17","first-page":"19","volume-title":"Lecture Notes on Computer Science","author":"P. Gritzmann","year":"1997","unstructured":"Gritzmann, P.: On the reconstruction of finite lattice sets from their X-rays. In: Ahronovitz, E., Fiorio,\u00a0C. (eds.) Lecture Notes on Computer Science, pp. 19\u201332. Springer, London (1997)"},{"key":"9213_CR18","doi-asserted-by":"crossref","first-page":"1894\u20131909","DOI":"10.1016\/j.ejc.2008.01.017","volume":"29","author":"P. Gritzmann","year":"2008","unstructured":"Gritzmann, P., Langfeld, B.: On the index of Siegel grids and its application to the tomography of quasicrystals. Eur. J. Comb. 29, 1894\u20131909 (2008)","journal-title":"Eur. J. Comb."},{"key":"9213_CR19","volume-title":"Discrete Tomography: Foundations, Algorithms, and Applications","year":"1999","unstructured":"Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms, and Applications. Birkh\u00e4user, Boston (1999)"},{"key":"9213_CR20","unstructured":"Huck, C.: Discrete tomography of delone sets with long-range order. Ph.D. thesis (Universit\u00e4t Bielefeld). Logos Verlag, Berlin (2007)"},{"key":"9213_CR21","unstructured":"Huck, C.: Uniqueness in discrete tomography of planar model sets, notes (2007). arXiv:math\/0701141v2 [math.MG]"},{"issue":"2","key":"9213_CR22","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.ejc.2008.05.001","volume":"30","author":"C. Huck","year":"2009","unstructured":"Huck, C.: A note on affinely regular polygons. Eur. J. Comb. 30(2), 387\u2013395 (2009). arXiv:0801.3218v1 [math.MG]","journal-title":"Eur. J. Comb."},{"key":"9213_CR23","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1107\/S0108767309004292","volume":"65","author":"C. Huck","year":"2009","unstructured":"Huck, C.: Discrete tomography of icosahedral model sets. Acta Crystallogr. A 65, 240\u2013248 (2009). arXiv:0705.3005v2 [math.MG]","journal-title":"Acta Crystallogr. A"},{"key":"9213_CR24","unstructured":"Huck, C.: On the existence of U-polygons of class c\u22654 in planar point sets. Discrete Math. (in press). arXiv:0811.3546v1 [math.MG]"},{"key":"9213_CR25","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0304-3991(94)00202-X","volume":"58","author":"C. Kisielowski","year":"1995","unstructured":"Kisielowski, C., Schwander, P., Baumann, F.H., Seibt, M., Kim, Y., Ourmazd, A.: An approach to quantitative high-resolution transmission electron microscopy of crystalline materials. Ultramicroscopy 58, 131\u2013155 (1995)","journal-title":"Ultramicroscopy"},{"key":"9213_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1112-9","volume-title":"p-adic Numbers, p-adic Analysis, and Zeta-Functions","author":"N. Koblitz","year":"1984","unstructured":"Koblitz, N.: p-adic Numbers, p-adic Analysis, and Zeta-Functions, 2nd edn. Springer, New York (1984)","edition":"2"},{"issue":"2","key":"9213_CR27","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/PL00009413","volume":"21","author":"J.C. Lagarias","year":"1999","unstructured":"Lagarias, J.C.: Geometric models for quasicrystals I. Delone sets of finite type. Discrete Comput. Geom. 21(2), 161\u2013191 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"9213_CR28","volume-title":"Algebra","author":"S. Lang","year":"1993","unstructured":"Lang, S.: Algebra, 3rd edn. Addison-Wesley, Reading (1993)","edition":"3"},{"key":"9213_CR29","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/978-3-662-04253-3_6","volume-title":"From Quasicrystals to More Complex Systems","author":"R.V. Moody","year":"2000","unstructured":"Moody, R.V.: Model sets: a survey. In: Axel, F., D\u00e9noyer, F., Gazeau, J.-P. (eds.) From Quasicrystals to More Complex Systems, pp. 145\u2013166. EDP Sciences, Les Ulis, and Springer, Berlin (2000). arXiv:math\/0002020v1 [math.MG]"},{"key":"9213_CR30","unstructured":"Pleasants, P.A.B.: Designer quasicrystals: cut-and-project sets with pre-assigned properties. In: [4], pp. 95\u2013141"},{"key":"9213_CR31","volume-title":"Algebraic Numbers and Fourier Analysis","author":"R. Salem","year":"1963","unstructured":"Salem, R.: Algebraic Numbers and Fourier Analysis. Heath, Boston (1963)"},{"key":"9213_CR32","series-title":"Fields Institute Monographs","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1090\/fim\/010\/09","volume-title":"Quasicrystals and Discrete Geometry","author":"M. Schlottmann","year":"1998","unstructured":"Schlottmann, M.: Cut-and-project sets in locally compact Abelian groups. In: Patera, J. (ed.) Quasicrystals and Discrete Geometry. Fields Institute Monographs, vol. 10, pp. 247\u2013264. AMS, Providence (1998)"},{"key":"9213_CR33","unstructured":"Schlottmann, M.: Generalized model sets and dynamical systems. In: [4], pp. 143\u2013159"},{"key":"9213_CR34","doi-asserted-by":"crossref","first-page":"4150","DOI":"10.1103\/PhysRevLett.71.4150","volume":"71","author":"P. Schwander","year":"1993","unstructured":"Schwander, P., Kisielowski, C., Seibt, M., Baumann, F.H., Kim, Y., Ourmazd, A.: Mapping projected potential, interfacial roughness, and composition in general crystalline solids by quantitative transmission electron microscopy. Phys. Rev. Lett. 71, 4150\u20134153 (1993)","journal-title":"Phys. Rev. Lett."},{"key":"9213_CR35","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1524\/zkri.219.7.391.35643","volume":"219","author":"W. Steurer","year":"2004","unstructured":"Steurer, W.: Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals. Z. Kristallogr. 219, 391\u2013446 (2004)","journal-title":"Z. Kristallogr."},{"key":"9213_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1934-7","volume-title":"Introduction to Cyclotomic Fields","author":"L.C. Washington","year":"1997","unstructured":"Washington, L.C.: Introduction to Cyclotomic Fields, 2nd edn. Springer, New York (1997)","edition":"2"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9213-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-009-9213-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9213-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T19:24:12Z","timestamp":1633721052000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-009-9213-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,17]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["9213"],"URL":"https:\/\/doi.org\/10.1007\/s00454-009-9213-z","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,17]]}}}