{"id":"https://openalex.org/W2131176118","doi":"https://doi.org/10.1007/978-3-540-77566-9_7","title":"On the Undecidability of the Tiling Problem","display_name":"On the Undecidability of the Tiling Problem","publication_year":2008,"publication_date":"2008-01-05","ids":{"openalex":"https://openalex.org/W2131176118","doi":"https://doi.org/10.1007/978-3-540-77566-9_7","mag":"2131176118"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-77566-9_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-77566-9_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057995798","display_name":"Jarkko Kari","orcid":"https://orcid.org/0000-0003-0670-6138"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jarkko Kari","raw_affiliation_strings":["Department of Mathematics, University of Turku, Finland","Department of mathematics, University of Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Turku, Finland","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"Department of mathematics, University of Turku, Finland","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057995798"],"corresponding_institution_ids":["https://openalex.org/I155660961"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.3861,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.63982055,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"74","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/square-tiling","display_name":"Square tiling","score":0.7067277431488037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.668559730052948},{"id":"https://openalex.org/keywords/hexagonal-tiling","display_name":"Hexagonal tiling","score":0.5461912155151367},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5395803451538086},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.537510335445404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.389691025018692},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3760022521018982},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3330006003379822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15217971801757812},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.13284331560134888}],"concepts":[{"id":"https://openalex.org/C178650486","wikidata":"https://www.wikidata.org/wiki/Q1128619","display_name":"Square tiling","level":3,"score":0.7067277431488037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.668559730052948},{"id":"https://openalex.org/C35908053","wikidata":"https://www.wikidata.org/wiki/Q3063631","display_name":"Hexagonal tiling","level":3,"score":0.5461912155151367},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5395803451538086},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.537510335445404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.389691025018692},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3760022521018982},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3330006003379822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15217971801757812},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.13284331560134888}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-77566-9_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-77566-9_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W16092949","https://openalex.org/W1588906418","https://openalex.org/W1886045675","https://openalex.org/W1990043417","https://openalex.org/W1990278318","https://openalex.org/W2013120724","https://openalex.org/W2017025480","https://openalex.org/W2021757832","https://openalex.org/W2050076818","https://openalex.org/W2080896750","https://openalex.org/W2113592921","https://openalex.org/W2161843469","https://openalex.org/W3159824982"],"related_works":["https://openalex.org/W3161130085","https://openalex.org/W4320480963","https://openalex.org/W2907672778","https://openalex.org/W1594480161","https://openalex.org/W1774734525","https://openalex.org/W2605413243","https://openalex.org/W4384920044","https://openalex.org/W1986012436","https://openalex.org/W2008223847","https://openalex.org/W1988821726"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
