{"id":"https://openalex.org/W2098253037","doi":"https://doi.org/10.1051/ita:2007018","title":"Defect theorem in the plane","display_name":"Defect theorem in the plane","publication_year":2007,"publication_date":"2007-08-17","ids":{"openalex":"https://openalex.org/W2098253037","doi":"https://doi.org/10.1051/ita:2007018","mag":"2098253037"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2007018","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007018","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","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/A5032141578","display_name":"W\u0142odzimierz Moczurad","orcid":null},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"W\u0142odzimierz Moczurad","raw_affiliation_strings":["Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Krak\u00f3w, Poland; wkm@ii.uj.edu.pl","Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Krak\u00f3w, Poland; wkm@ii.uj.edu.pl","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032141578"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210087266"],"apc_list":null,"apc_paid":null,"fwci":1.4572,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82442524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"41","issue":"4","first_page":"403","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7307984232902527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6680898070335388},{"id":"https://openalex.org/keywords/polyomino","display_name":"Polyomino","score":0.6432695388793945},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.61876380443573},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5950667858123779},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5856404304504395},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5436110496520996},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5393834114074707},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4559224247932434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44286638498306274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15145158767700195},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1082768440246582},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.060929715633392334}],"concepts":[{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7307984232902527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6680898070335388},{"id":"https://openalex.org/C69919132","wikidata":"https://www.wikidata.org/wiki/Q1144819","display_name":"Polyomino","level":3,"score":0.6432695388793945},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.61876380443573},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5950667858123779},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5856404304504395},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5436110496520996},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5393834114074707},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4559224247932434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44286638498306274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15145158767700195},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1082768440246582},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.060929715633392334},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita:2007018","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2007018","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2007__41_4_403_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2007018/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W815150804","https://openalex.org/W1526262596","https://openalex.org/W1541480695","https://openalex.org/W1586417893","https://openalex.org/W1922096600","https://openalex.org/W2018171227","https://openalex.org/W2045745341","https://openalex.org/W2047972554","https://openalex.org/W2053863683","https://openalex.org/W2063941709","https://openalex.org/W2064947749","https://openalex.org/W2073286366","https://openalex.org/W2912263704","https://openalex.org/W4231199984"],"related_works":["https://openalex.org/W4288734188","https://openalex.org/W209156724","https://openalex.org/W2135008840","https://openalex.org/W148666007","https://openalex.org/W2103874366","https://openalex.org/W2572231869","https://openalex.org/W2962715651","https://openalex.org/W2119324012","https://openalex.org/W4300904684","https://openalex.org/W1974628954"],"abstract_inverted_index":{"We":[0,54],"consider":[1],"the":[2,6,33,48,60,63,70,74],"defect":[3,71],"theorem":[4,64],"in":[5,73],"context":[7],"of":[8,17,25,41,76],"labelled":[9],"polyominoes,":[10],"i.e.,":[11],"two-dimensional":[12,57],"figures.":[13],"The":[14],"classical":[15],"version":[16],"this":[18],"property":[19,72],"states":[20],"that":[21],"if":[22],"a":[23,30,39,52],"set":[24,50],"n":[26,44,85],"words":[27,34],"is":[28],"not":[29],"code":[31],"then":[32],"can":[35],"be":[36],"expressed":[37],"as":[38],"product":[40],"at":[42],"most":[43],"-":[45],"1":[46,81,83],"words,":[47],"smaller":[49],"being":[51],"code.":[53],"survey":[55],"several":[56],"extensions":[58],"exhibiting":[59],"boundaries":[61],"where":[62],"fails.":[65],"In":[66],"particular,":[67],"we":[68],"establish":[69],"case":[75],"three":[77],"dominoes":[78],"(n":[79],"\u00d7":[80,84],"or":[82],"rectangles).":[86]},"counts_by_year":[{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
