{"id":"https://openalex.org/W2962926152","doi":"https://doi.org/10.1007/s00373-018-1967-8","title":"Perfect k-Colored Matchings and $$(k+2)$$ ( k + 2 ) -Gonal Tilings","display_name":"Perfect k-Colored Matchings and $$(k+2)$$ ( k + 2 ) -Gonal Tilings","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2962926152","doi":"https://doi.org/10.1007/s00373-018-1967-8","mag":"2962926152","pmid":"https://pubmed.ncbi.nlm.nih.gov/31929681"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-018-1967-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-018-1967-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-018-1967-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-018-1967-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091823049","display_name":"Oswin Aichholzer","orcid":"https://orcid.org/0000-0002-2364-0583"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Oswin Aichholzer","raw_affiliation_strings":["1Institute of Software Technology, Graz University of Technology, Graz, Austria","Institute of Software Technology, Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"1Institute of Software Technology, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Institute of Software Technology, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110671834","display_name":"Lukas Andritsch","orcid":null},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I202276237","display_name":"Medical University of Graz","ror":"https://ror.org/02n0bts35","country_code":"AT","type":"education","lineage":["https://openalex.org/I202276237"]},{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Lukas Andritsch","raw_affiliation_strings":["2Mathematics and Scientific Computing, University of Graz, Graz, Austria","Mathematics and Scientific Computing, University of Graz, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"2Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I202276237","https://openalex.org/I4092182"]},{"raw_affiliation_string":"Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038338025","display_name":"Karin Baur","orcid":"https://orcid.org/0000-0002-7665-476X"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I202276237","display_name":"Medical University of Graz","ror":"https://ror.org/02n0bts35","country_code":"AT","type":"education","lineage":["https://openalex.org/I202276237"]},{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karin Baur","raw_affiliation_strings":["2Mathematics and Scientific Computing, University of Graz, Graz, Austria","Mathematics and Scientific Computing, University of Graz, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"2Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I202276237","https://openalex.org/I4092182"]},{"raw_affiliation_string":"Mathematics and Scientific Computing, University of Graz, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073288056","display_name":"Birgit Vogtenhuber","orcid":"https://orcid.org/0000-0002-7166-4467"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Birgit Vogtenhuber","raw_affiliation_strings":["1Institute of Software Technology, Graz University of Technology, Graz, Austria","Institute of Software Technology, Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"1Institute of Software Technology, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]},{"raw_affiliation_string":"Institute of Software Technology, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073288056"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.5194,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.82783036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"34","issue":"6","first_page":"1333","last_page":"1346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8607043027877808},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.835157036781311},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8128520250320435},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.7005341649055481},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.6022884249687195},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5432624816894531},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5424668192863464},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.5134321451187134},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47216030955314636},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.45464974641799927},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.43153083324432373},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3261146545410156},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13068628311157227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07484191656112671}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8607043027877808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.835157036781311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8128520250320435},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.7005341649055481},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.6022884249687195},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5432624816894531},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5424668192863464},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.5134321451187134},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47216030955314636},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.45464974641799927},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.43153083324432373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3261146545410156},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13068628311157227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07484191656112671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00373-018-1967-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-018-1967-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-018-1967-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmid:31929681","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31929681","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and combinatorics","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:6936358","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6936358","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Graphs Comb","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00373-018-1967-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-018-1967-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-018-1967-8.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3288250452","display_name":null,"funder_award_id":"W1230.","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4135731702","display_name":null,"funder_award_id":"W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962926152.pdf","grobid_xml":"https://content.openalex.org/works/W2962926152.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1986188777","https://openalex.org/W2101868700","https://openalex.org/W2137459590","https://openalex.org/W2155365991","https://openalex.org/W2164779253","https://openalex.org/W2751862591","https://openalex.org/W3102604173","https://openalex.org/W4301441647"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W2806276129","https://openalex.org/W4299611798","https://openalex.org/W1893226401","https://openalex.org/W2885368579","https://openalex.org/W2030568854","https://openalex.org/W2110957471","https://openalex.org/W2952466037","https://openalex.org/W2015282370"],"abstract_inverted_index":{"We":[0,28],"derive":[1],"a":[2,61,79],"simple":[3],"bijection":[4,32],"between":[5,73],"geometric":[6],"plane":[7,35],"perfect":[8,36],"matchings":[9,37,74],"on":[10,18,38],"2<i>n</i>":[11],"points":[12,24],"in":[13,25,95],"convex":[14,26,53],"position":[15],"and":[16,42,66,75],"triangulations":[17],"<mml:math":[19,43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>n</mml:mi>":[20],"<mml:mo>+</mml:mo>":[21,46],"<mml:mn>2</mml:mn></mml:mrow>":[22],"</mml:math>":[23,49],"position.":[27],"then":[29],"extend":[30],"this":[31],"to":[33,60],"monochromatic":[34],"periodically":[39],"<i>k</i>-colored":[40],"vertices":[41],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mo>(</mml:mo>":[44],"<mml:mi>k</mml:mi>":[45],"<mml:mn>2</mml:mn>":[47],"<mml:mo>)</mml:mo></mml:mrow>":[48],"-gonal":[50],"tilings":[51],"of":[52,63,82,88],"point":[54],"sets.":[55],"These":[56],"structures":[57],"are":[58],"related":[59],"generalization":[62],"Temperley-Lieb":[64],"algebras":[65],"our":[67],"bijections":[68],"provide":[69],"explicit":[70],"one-to-one":[71],"relations":[72],"tilings.":[76],"Moreover,":[77],"for":[78],"given":[80],"element":[81,87],"one":[83],"class,":[84],"the":[85,89],"corresponding":[86],"other":[90],"class":[91],"can":[92],"be":[93],"computed":[94],"linear":[96],"time.":[97]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-07-30T00:00:00"}
