{"id":"https://openalex.org/W1592656152","doi":"https://doi.org/10.37236/489","title":"Subplanes of Order $3$ in Hughes Planes","display_name":"Subplanes of Order $3$ in Hughes Planes","publication_year":2011,"publication_date":"2011-01-05","ids":{"openalex":"https://openalex.org/W1592656152","doi":"https://doi.org/10.37236/489","mag":"1592656152"},"language":"en","primary_location":{"id":"doi:10.37236/489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p2/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/v18i1p2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010706666","display_name":"Cafer \u00c7al\u0131\u015fkan","orcid":"https://orcid.org/0000-0002-9619-9207"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cafer Caliskan","raw_affiliation_strings":[", Michigan Technological University"],"affiliations":[{"raw_affiliation_string":", Michigan Technological University","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055178916","display_name":"G. Eric Moorhouse","orcid":"https://orcid.org/0000-0001-5001-0045"},"institutions":[{"id":"https://openalex.org/I4210116506","display_name":"Wyoming Department of Education","ror":"https://ror.org/02abxwv41","country_code":"US","type":"government","lineage":["https://openalex.org/I4210116506"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Eric Moorhouse","raw_affiliation_strings":["university of Wyoming"],"affiliations":[{"raw_affiliation_string":"university of Wyoming","institution_ids":["https://openalex.org/I4210116506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010706666"],"corresponding_institution_ids":["https://openalex.org/I11957088"],"apc_list":null,"apc_paid":null,"fwci":0.5403,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68621562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8405497074127197},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.7426413893699646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6953172087669373},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5774385929107666},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5768776535987854},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.4341218173503876},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37655147910118103},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2063365876674652}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8405497074127197},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.7426413893699646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6953172087669373},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5774385929107666},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5768776535987854},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.4341218173503876},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37655147910118103},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2063365876674652},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p2/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"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-33430","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/14127","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.460.3944","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.3944","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p2/pdf/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.601.2070","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.601.2070","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uwyo.edu/moorhouse/pub/subplane3.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/489","is_oa":true,"landing_page_url":"https://doi.org/10.37236/489","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p2/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1592656152.pdf","grobid_xml":"https://content.openalex.org/works/W1592656152.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W7833276","https://openalex.org/W1585954501","https://openalex.org/W1594156290","https://openalex.org/W1770257966","https://openalex.org/W1918858098","https://openalex.org/W1964031658","https://openalex.org/W1974457501","https://openalex.org/W1978070273","https://openalex.org/W1979612878","https://openalex.org/W2005448739","https://openalex.org/W2005672194","https://openalex.org/W2007176934","https://openalex.org/W2009751674","https://openalex.org/W2016168720","https://openalex.org/W2040295871","https://openalex.org/W2049587182","https://openalex.org/W2066315811","https://openalex.org/W2079121590","https://openalex.org/W2091415780","https://openalex.org/W2091717311","https://openalex.org/W2095442212","https://openalex.org/W2621250977","https://openalex.org/W2915069140","https://openalex.org/W4252500359"],"related_works":["https://openalex.org/W2543275399","https://openalex.org/W1998402533","https://openalex.org/W2069443110","https://openalex.org/W2292792029","https://openalex.org/W860790991","https://openalex.org/W4302423208","https://openalex.org/W4380141713","https://openalex.org/W2177966018","https://openalex.org/W36763073","https://openalex.org/W2748002572"],"abstract_inverted_index":{"In":[0],"this":[1],"study":[2],"we":[3],"show":[4,34],"the":[5],"existence":[6],"of":[7,9,15],"subplanes":[8],"order":[10,16],"$3$":[11],"in":[12,45],"Hughes":[13,47],"planes":[14],"$q^2$,":[17],"where":[18],"$q$":[19],"is":[20],"a":[21],"prime":[22],"power":[23],"and":[24],"$q":[25],"\\equiv":[26],"5":[27],"\\":[28,30],"(mod":[29],"6)$.":[31],"We":[32],"further":[33],"that":[35],"there":[36],"exist":[37],"finite":[38],"partial":[39],"linear":[40],"spaces":[41],"which":[42],"cannot":[43],"embed":[44],"any":[46],"plane.":[48]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
