{"id":"https://openalex.org/W1589924350","doi":"https://doi.org/10.37236/4227","title":"Multiple Coverings with Closed Polygons","display_name":"Multiple Coverings with Closed Polygons","publication_year":2015,"publication_date":"2015-01-27","ids":{"openalex":"https://openalex.org/W1589924350","doi":"https://doi.org/10.37236/4227","mag":"1589924350"},"language":"en","primary_location":{"id":"doi:10.37236/4227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p18/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101539917","display_name":"Istv\u00e1n Kov\u00e1cs","orcid":"https://orcid.org/0000-0002-4902-3559"},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Istv\u00e1n Kov\u00e1cs","raw_affiliation_strings":["Budapest University of Technology and Economics","Budapest Univ. of Technology & Economics"],"affiliations":[{"raw_affiliation_string":"Budapest University of Technology and Economics","institution_ids":["https://openalex.org/I29770179"]},{"raw_affiliation_string":"Budapest Univ. of Technology & Economics","institution_ids":["https://openalex.org/I29770179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103265930","display_name":"G\u00e9z\u00e1 T\u00f3th","orcid":"https://orcid.org/0000-0003-1751-6911"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"G\u00e9za T\u00f3th","raw_affiliation_strings":["Renyi Institute, Hungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Renyi Institute, Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101539917"],"corresponding_institution_ids":["https://openalex.org/I29770179"],"apc_list":null,"apc_paid":null,"fwci":0.8869,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78215704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11870","display_name":"Structural Analysis and Optimization","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/regular-polygon","display_name":"Regular polygon","score":0.7493493556976318},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.7157108783721924},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7010417580604553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.682304859161377},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6748148202896118},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6551951169967651},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42618095874786377},{"id":"https://openalex.org/keywords/fold","display_name":"Fold (higher-order function)","score":0.42506328225135803},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4227655231952667},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4225793480873108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12595641613006592},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.06795802712440491}],"concepts":[{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7493493556976318},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.7157108783721924},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7010417580604553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.682304859161377},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6748148202896118},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6551951169967651},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42618095874786377},{"id":"https://openalex.org/C53942344","wikidata":"https://www.wikidata.org/wiki/Q951651","display_name":"Fold (higher-order function)","level":2,"score":0.42506328225135803},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4227655231952667},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4225793480873108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12595641613006592},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.06795802712440491},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/4227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:176636","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1403.2653","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.2653","pdf_url":"https://arxiv.org/pdf/1403.2653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:1589924350","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1403.2653.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1403.2653","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1403.2653","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/4227","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4227","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p18/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1529973407","display_name":null,"funder_award_id":"K-83767","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G1808771523","display_name":null,"funder_award_id":"OTKA NN 102029","funder_id":"https://openalex.org/F4320326184","funder_display_name":"Hungarian Science Foundation"},{"id":"https://openalex.org/G3839487825","display_name":null,"funder_award_id":"NN 102029","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G5864815688","display_name":null,"funder_award_id":"OTKA NN 102029","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"},{"id":"https://openalex.org/G7374383311","display_name":null,"funder_award_id":"OTKA K","funder_id":"https://openalex.org/F4320321994","funder_display_name":"Hungarian Scientific Research Fund"}],"funders":[{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320326184","display_name":"Hungarian Science Foundation","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1589924350.pdf","grobid_xml":"https://content.openalex.org/works/W1589924350.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7428044"],"related_works":["https://openalex.org/W2963566351","https://openalex.org/W2951163544","https://openalex.org/W2559490119","https://openalex.org/W1932931411","https://openalex.org/W2143341942","https://openalex.org/W2951754898","https://openalex.org/W2912897063","https://openalex.org/W2220719914","https://openalex.org/W2048906036","https://openalex.org/W1673739447","https://openalex.org/W2110431853","https://openalex.org/W1584699731","https://openalex.org/W2185983738","https://openalex.org/W2119790501","https://openalex.org/W2740243938","https://openalex.org/W1972194040","https://openalex.org/W22225833","https://openalex.org/W2686396252","https://openalex.org/W2056491846","https://openalex.org/W2912348711"],"abstract_inverted_index":{"A":[0],"planar":[1],"set":[2],"$P$":[3,26,67],"is":[4,11,34],"said":[5],"to":[6],"be":[7,28,69],"cover-decomposable":[8],"if":[9],"there":[10],"a":[12],"constant":[13],"$k=k(P)$":[14],"such":[15],"that":[16,36,45,57],"every":[17],"$k$-fold":[18],"covering":[19,60],"of":[20,25,61,66,80,83],"the":[21,62,84],"plane":[22,63],"with":[23,64],"translates":[24,65],"can":[27,68],"decomposed":[29,70],"into":[30,71],"two":[31,72],"coverings.":[32,74],"It":[33],"known":[35],"open":[37],"convex":[38,49],"polygons":[39,50],"are":[40,51],"cover-decomposable.":[41,53],"Here":[42],"we":[43],"show":[44,56],"closed,":[46],"centrally":[47],"symmetric":[48],"also":[52,55],"We":[54],"an":[58],"infinite-fold":[59,73],"Both":[75],"results":[76],"hold":[77],"for":[78],"coverings":[79],"any":[81],"subset":[82],"plane.":[85]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}