{"id":"https://openalex.org/W2096398399","doi":"https://doi.org/10.37236/557","title":"Counting Triangulations of Planar Point Sets","display_name":"Counting Triangulations of Planar Point Sets","publication_year":2011,"publication_date":"2011-03-31","ids":{"openalex":"https://openalex.org/W2096398399","doi":"https://doi.org/10.37236/557","mag":"2096398399"},"language":"en","primary_location":{"id":"doi:10.37236/557","is_oa":true,"landing_page_url":"https://doi.org/10.37236/557","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p70/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p70/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["Tel-Aviv  University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038764657","display_name":"Adam Sheffer","orcid":"https://orcid.org/0000-0003-3418-5122"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Adam Sheffer","raw_affiliation_strings":["Tel-Aviv  University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":23.7438,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":{"value":0.99666944,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","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":0.9998999834060669,"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":0.9998999834060669,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9966999888420105,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8896657228469849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8361537456512451},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7998149394989014},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6512259840965271},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6497483253479004},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6442751288414001},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.5912895798683167},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5083476901054382},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47624754905700684},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38885098695755005},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21330246329307556},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10233944654464722},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07514899969100952}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8896657228469849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8361537456512451},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7998149394989014},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6512259840965271},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6497483253479004},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6442751288414001},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5912895798683167},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5083476901054382},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47624754905700684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38885098695755005},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21330246329307556},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10233944654464722},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07514899969100952},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/557","is_oa":true,"landing_page_url":"https://doi.org/10.37236/557","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p70/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/557","is_oa":true,"landing_page_url":"https://doi.org/10.37236/557","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p70/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":null,"license_id":null,"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/G1227625532","display_name":null,"funder_award_id":"CCF-08-30272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2096398399.pdf","grobid_xml":"https://content.openalex.org/works/W2096398399.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W22200857","https://openalex.org/W43719964","https://openalex.org/W146417191","https://openalex.org/W574460519","https://openalex.org/W575055273","https://openalex.org/W1551177513","https://openalex.org/W1567268701","https://openalex.org/W1597152871","https://openalex.org/W1656795039","https://openalex.org/W1773540271","https://openalex.org/W1788866689","https://openalex.org/W1817632074","https://openalex.org/W1965976352","https://openalex.org/W1988809014","https://openalex.org/W1996008071","https://openalex.org/W2029387472","https://openalex.org/W2030997953","https://openalex.org/W2032773290","https://openalex.org/W2057690024","https://openalex.org/W2069225643","https://openalex.org/W2085179971","https://openalex.org/W2089078292","https://openalex.org/W2114928211","https://openalex.org/W2132345770","https://openalex.org/W2134147092","https://openalex.org/W2148360835","https://openalex.org/W2157274506","https://openalex.org/W2160689382","https://openalex.org/W2161968825","https://openalex.org/W2163448076","https://openalex.org/W2205343714","https://openalex.org/W2914659449","https://openalex.org/W2952537829","https://openalex.org/W2952626446","https://openalex.org/W2952780231","https://openalex.org/W3134545872","https://openalex.org/W4243262670","https://openalex.org/W4301890399","https://openalex.org/W4388438965","https://openalex.org/W6609665257"],"related_works":["https://openalex.org/W1984006984","https://openalex.org/W2132137594","https://openalex.org/W2069783012","https://openalex.org/W2085967955","https://openalex.org/W4256335355","https://openalex.org/W3098612666","https://openalex.org/W1499116563","https://openalex.org/W2138867060","https://openalex.org/W2023859141","https://openalex.org/W2182290077"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,34,46,54,64,91],"maximal":[3],"number":[4,65,92],"of":[5,11,33,37,51,66,69,93],"triangulations":[6],"that":[7,18],"a":[8,30,76],"planar":[9,70,94],"set":[10],"$n$":[12],"points":[13],"can":[14,82],"have,":[15],"and":[16,39,103],"show":[17],"it":[19,81],"is":[20,27,60],"at":[21],"most":[22],"$30^n$.":[23],"This":[24],"new":[25,58,87],"bound":[26,50,59],"achieved":[28],"by":[29],"careful":[31],"optimization":[32],"charging":[35],"scheme":[36],"Sharir":[38],"Welzl":[40],"(2006),":[41],"which":[42],"has":[43],"led":[44],"to":[45,85],"previous":[47],"best":[48],"upper":[49,88],"$43^n$":[52],"for":[53,62,90],"problem.":[55],"Moreover,":[56],"this":[57],"useful":[61],"bounding":[63],"other":[67],"types":[68],"(i.e.,":[71],"crossing-free)":[72],"straight-line":[73],"graphs":[74,95,105],"on":[75],"given":[77],"point":[78],"set.":[79],"Specifically,":[80],"be":[83],"used":[84],"derive":[86],"bounds":[89],"($207.84^n$),":[96],"spanning":[97,100],"cycles":[98],"($O(68.67^n)$),":[99],"trees":[101],"($O(146.69^n)$),":[102],"cycle-free":[104],"($O(164.17^n)$).":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}