{"id":"https://openalex.org/W3208964976","doi":"https://doi.org/10.37236/9890","title":"Counting Non-Crossing Permutations on Surfaces of any Genus","display_name":"Counting Non-Crossing Permutations on Surfaces of any Genus","publication_year":2021,"publication_date":"2021-10-21","ids":{"openalex":"https://openalex.org/W3208964976","doi":"https://doi.org/10.37236/9890","mag":"3208964976"},"language":"en","primary_location":{"id":"doi:10.37236/9890","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9890","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p9/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":"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/v28i4p9/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039939209","display_name":"Norman Do","orcid":"https://orcid.org/0000-0002-2135-978X"},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Norman Do","raw_affiliation_strings":["Monash University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045172769","display_name":"Jian He","orcid":null},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jian He","raw_affiliation_strings":["Monash University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007864871","display_name":"Daniel V. Mathews","orcid":"https://orcid.org/0000-0003-3468-5039"},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daniel V. Mathews","raw_affiliation_strings":["Monash University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31752963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9973000288009644,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9947999715805054,"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/mathematics","display_name":"Mathematics","score":0.8170270919799805},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.7565926313400269},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7546895742416382},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.6658066511154175},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6535260677337646},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.617077112197876},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.615975022315979},{"id":"https://openalex.org/keywords/newton-polygon","display_name":"Newton polygon","score":0.6149498820304871},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.5812963247299194},{"id":"https://openalex.org/keywords/moduli-space","display_name":"Moduli space","score":0.5811312794685364},{"id":"https://openalex.org/keywords/polygon-covering","display_name":"Polygon covering","score":0.5731644630432129},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4599091410636902},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.4513307809829712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2758864164352417},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.2703656554222107},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11688297986984253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06573545932769775}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8170270919799805},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.7565926313400269},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7546895742416382},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6658066511154175},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6535260677337646},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.617077112197876},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.615975022315979},{"id":"https://openalex.org/C2777684946","wikidata":"https://www.wikidata.org/wiki/Q115646","display_name":"Newton polygon","level":2,"score":0.6149498820304871},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5812963247299194},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.5811312794685364},{"id":"https://openalex.org/C187778580","wikidata":"https://www.wikidata.org/wiki/Q18389289","display_name":"Polygon covering","level":3,"score":0.5731644630432129},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4599091410636902},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.4513307809829712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2758864164352417},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.2703656554222107},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11688297986984253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06573545932769775},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9890","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9890","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p9/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"}],"best_oa_location":{"id":"doi:10.37236/9890","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9890","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p9/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208964976.pdf","grobid_xml":"https://content.openalex.org/works/W3208964976.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W76426102","https://openalex.org/W1526007200","https://openalex.org/W1663131564","https://openalex.org/W1954611934","https://openalex.org/W1967396208","https://openalex.org/W1969959148","https://openalex.org/W1972563066","https://openalex.org/W1973953053","https://openalex.org/W1986412636","https://openalex.org/W2006442667","https://openalex.org/W2028897994","https://openalex.org/W2044115033","https://openalex.org/W2119172254","https://openalex.org/W2143056798","https://openalex.org/W2152585937","https://openalex.org/W2740772262","https://openalex.org/W2950117051","https://openalex.org/W2963512285","https://openalex.org/W2963578722","https://openalex.org/W2963828036","https://openalex.org/W3098135146","https://openalex.org/W3104262622","https://openalex.org/W6602285270","https://openalex.org/W6832503667"],"related_works":["https://openalex.org/W2734824228","https://openalex.org/W321614567","https://openalex.org/W2466150543","https://openalex.org/W2362048241","https://openalex.org/W2379265227","https://openalex.org/W2608536130","https://openalex.org/W2353856915","https://openalex.org/W2239436216","https://openalex.org/W2389833224","https://openalex.org/W2953227767"],"abstract_inverted_index":{"Given":[0],"a":[1,11,15,57],"surface":[2],"with":[3,70],"boundary":[4,76,94],"and":[5,73,96],"some":[6],"points":[7,20,91],"on":[8,26,35,68,92,106],"the":[9,27,36,46,63,88,93,97],"boundary,":[10],"polygon":[12,30,66],"diagram":[13],"is":[14,53,84],"way":[16],"to":[17,55],"connect":[18],"those":[19,101],"as":[21],"vertices":[22],"of":[23,48,65,75,90,100,110],"non-overlapping":[24],"polygons":[25],"surface.":[28,37],"Such":[29],"diagrams":[31,67],"represent":[32],"non-crossing":[33],"permutations":[34],"If":[38],"only":[39],"bigons":[40],"are":[41,103],"allowed,":[42],"then":[43],"one":[44],"obtains":[45],"notion":[47],"arc":[49],"diagrams,":[50],"whose":[51],"enumeration":[52],"known":[54],"have":[56],"rich":[58],"structure.":[59,80],"We":[60],"show":[61],"that":[62],"count":[64],"surfaces":[69],"any":[71],"genus":[72],"number":[74,89],"components":[77],"exhibits":[78],"similar":[79],"In":[81],"particular":[82],"it":[83],"almost":[85],"polynomial":[86],"in":[87],"components,":[95],"leading":[98],"coefficients":[99],"polynomials":[102],"intersection":[104],"numbers":[105],"compactified":[107],"moduli":[108],"spaces":[109],"curves.":[111]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}