{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T12:42:21Z","timestamp":1789994541264,"version":"4.0.1"},"publisher-location":"Cham","reference-count":13,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319230207","type":"print"},{"value":"9783319230214","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-23021-4_3","type":"book-chapter","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T20:47:30Z","timestamp":1441745250000},"page":"29-42","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Algebraic Geometric Approach to Multidimensional Words"],"prefix":"10.1007","author":[{"given":"Jarkko","family":"Kari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michal","family":"Szabados","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,9,9]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Beauquier, D., Nivat, M.: On Translating One Polyomino to Tile the Plane. Discrete & Computational Geometry 6 (1991)","DOI":"10.1007\/BF02574705"},{"key":"3_CR2","unstructured":"Cyr, V., Kra, B.: Complexity of short rectangles and periodicity (2013) (submitted). arXiv: 1307.0098 [math.DS]"},{"key":"3_CR3","unstructured":"Cyr, V., Kra, B.: Nonexpansive \n$$\\mathbb{Z}^{2}$$\n-subdynamics and Nivat\u2019s conjecture. Trans. Amer. Math. Soc. (2013) (to appear)"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Epifanio, C., Koskas, M., Mignosi, F.: On a conjecture on bidimensional words. Theor. Comput. Sci. (1\u20133), 299 (2003)","DOI":"10.1016\/S0304-3975(01)00386-3"},{"key":"3_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/978-3-662-47666-6_22","volume-title":"Automata, Languages, and Programming","author":"Jarkko Kari","year":"2015","unstructured":"Kari, Jarkko, Szabados, Michal: An algebraic geometric approach to nivat\u2019s conjecture. In: Halld\u00f3rsson, Magn\u00fas M., Iwama, Kazuo, Kobayashi, Naoki, Speckmann, Bettina (eds.) ICALP 2015. LNCS, vol. 9135, pp. 273\u2013285. Springer, Heidelberg (2015)"},{"key":"3_CR6","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s002220050056","volume":"124","author":"JC Lagarias","year":"1996","unstructured":"Lagarias, J.C., Wang, Y.: Tiling the Line with Translates of One Tile. Inventiones Mathematicae 124, 341\u2013365 (1996)","journal-title":"Inventiones Mathematicae"},{"key":"3_CR7","doi-asserted-by":"crossref","unstructured":"Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press (1995)","DOI":"10.1017\/CBO9780511626302"},{"issue":"4","key":"3_CR8","doi-asserted-by":"publisher","first-page":"815","DOI":"10.2307\/2371264","volume":"60","author":"M Morse","year":"1938","unstructured":"Morse, M., Hedlund, G.A.: Symbolic Dynamics. American Journal of Mathematics 60(4), 815\u2013866 (1938)","journal-title":"American Journal of Mathematics"},{"key":"3_CR9","unstructured":"Nivat, M.: Invited talk at ICALP, Bologna (1997)"},{"issue":"1\u20133","key":"3_CR10","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/j.tcs.2004.02.026","volume":"319","author":"A Quas","year":"2004","unstructured":"Quas, A., Zamboni, L.Q.: Periodicity and local complexity. Theor. Comput. Sci. 319(1\u20133), 229\u2013240 (2004)","journal-title":"Theor. Comput. Sci."},{"issue":"1\u20132","key":"3_CR11","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S0304-3975(99)00078-X","volume":"246","author":"JW Sander","year":"2000","unstructured":"Sander, J.W., Tijdeman, R.: The complexity of functions on lattices. Theor. Comput. Sci. 246(1\u20132), 195\u2013225 (2000)","journal-title":"Theor. Comput. Sci."},{"issue":"1\u20132","key":"3_CR12","doi-asserted-by":"publisher","first-page":"857","DOI":"10.1016\/S0304-3975(01)00281-X","volume":"270","author":"JW Sander","year":"2002","unstructured":"Sander, J.W., Tijdeman, R.: The rectangle complexity of functions on two-dimensional lattices. Theor. Comput. Sci. 270(1\u20132), 857\u2013863 (2002)","journal-title":"Theor. Comput. Sci."},{"key":"3_CR13","unstructured":"Szegedy, M.: Algorithms to tile the infnite grid with finite clusters. In: FOCS, pp. 137\u2013147. IEEE Computer Society (1998)"}],"container-title":["Lecture Notes in Computer Science","Algebraic Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-23021-4_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T11:26:09Z","timestamp":1676978769000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-23021-4_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319230207","9783319230214"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-23021-4_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"9 September 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}