{"id":"https://openalex.org/W3000527422","doi":"https://doi.org/10.37236/7589","title":"Classification of the Hyperovals in PG(2,64)","display_name":"Classification of the Hyperovals in PG(2,64)","publication_year":2019,"publication_date":"2019-05-31","ids":{"openalex":"https://openalex.org/W3000527422","doi":"https://doi.org/10.37236/7589","mag":"3000527422"},"language":"en","primary_location":{"id":"doi:10.37236/7589","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7589","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p35/7849","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/v26i2p35/7849","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083955784","display_name":"Peter Vandendriessche","orcid":"https://orcid.org/0000-0002-3407-6439"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Peter Vandendriessche","raw_affiliation_strings":["Ghent University"],"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083955784"],"corresponding_institution_ids":["https://openalex.org/I2801227569"],"apc_list":null,"apc_paid":null,"fwci":2.5406,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89268604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9976999759674072,"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/T10849","display_name":"Finite Group Theory Research","score":0.9976999759674072,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9800999760627747,"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/T11215","display_name":"Chronic Myeloid Leukemia Treatments","score":0.9592000246047974,"subfield":{"id":"https://openalex.org/subfields/2720","display_name":"Hematology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.832060694694519},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7984514832496643},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7849873304367065},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.7803000807762146},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.584547758102417},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5614308714866638},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.47878921031951904},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.41546013951301575},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3269604444503784},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11649703979492188},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.06534305214881897}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.832060694694519},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7984514832496643},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7849873304367065},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.7803000807762146},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.584547758102417},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5614308714866638},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.47878921031951904},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.41546013951301575},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3269604444503784},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11649703979492188},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.06534305214881897},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7589","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7589","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p35/7849","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:10.37236/7589","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7589","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p35/7849","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/G3231420740","display_name":null,"funder_award_id":"postdoc","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000527422.pdf","grobid_xml":"https://content.openalex.org/works/W3000527422.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W37470867","https://openalex.org/W2028572867","https://openalex.org/W2086522968","https://openalex.org/W2129097704","https://openalex.org/W2129652965","https://openalex.org/W2135890456","https://openalex.org/W2142636032","https://openalex.org/W2334224849","https://openalex.org/W2912214852","https://openalex.org/W3000527422","https://openalex.org/W6668303705","https://openalex.org/W6679757108","https://openalex.org/W6702930940","https://openalex.org/W6758734929"],"related_works":["https://openalex.org/W2040976798","https://openalex.org/W2356676145","https://openalex.org/W2382326160","https://openalex.org/W2554495525","https://openalex.org/W2358939236","https://openalex.org/W2239330273","https://openalex.org/W2371953206","https://openalex.org/W2047714933","https://openalex.org/W2093858167","https://openalex.org/W2349543044"],"abstract_inverted_index":{"In":[0],"this":[1,30],"paper,":[2],"we":[3],"present":[4],"a":[5,50],"full":[6],"classification":[7],"of":[8,53],"the":[9,12],"hyperovals":[10],"in":[11,49],"finite":[13],"projective":[14],"plane":[15],"$\\mathrm{PG}(2,64)$,":[16],"showing":[17],"that":[18],"there":[19],"are":[20],"exactly":[21],"4":[22],"isomorphism":[23],"classes.":[24],"The":[25],"techniques":[26],"developed":[27],"to":[28,37],"obtain":[29],"result":[31],"can":[32],"be":[33],"applied":[34],"more":[35],"generally":[36],"classify":[38],"point":[39],"sets":[40],"with":[41],"$0$":[42],"or":[43],"$2$":[44],"points":[45],"on":[46],"every":[47],"line,":[48],"broad":[51],"range":[52],"highly":[54],"symmetric":[55],"incidence":[56],"structures.":[57]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}