{"id":"https://openalex.org/W4400196885","doi":"https://doi.org/10.5070/c64163845","title":"Sets of mutually orthogoval projective and affine planes","display_name":"Sets of mutually orthogoval projective and affine planes","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4400196885","doi":"https://doi.org/10.5070/c64163845"},"language":"en","primary_location":{"id":"doi:10.5070/c64163845","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64163845","pdf_url":"https://escholarship.org/content/qt6q20z7sg/qt6q20z7sg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt6q20z7sg/qt6q20z7sg.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038008468","display_name":"Charles J. Colbourn","orcid":"https://orcid.org/0000-0002-3104-9515"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Charles J. Colbourn","raw_affiliation_strings":["School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85287-8809, U.S.A"],"affiliations":[{"raw_affiliation_string":"School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ 85287-8809, U.S.A","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038022297","display_name":"Colin Ingalls","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Colin Ingalls","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035429068","display_name":"Jonathan Jedwab","orcid":"https://orcid.org/0000-0001-5296-9700"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jonathan Jedwab","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006689325","display_name":"Mark Saaltink","orcid":"https://orcid.org/0000-0003-2963-603X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Saaltink","raw_affiliation_strings":["Independent"],"affiliations":[{"raw_affiliation_string":"Independent","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090201337","display_name":"K. Smith","orcid":"https://orcid.org/0000-0001-9535-3199"},"institutions":[{"id":"https://openalex.org/I191429286","display_name":"Sam Houston State University","ror":"https://ror.org/00yh3cz06","country_code":"US","type":"education","lineage":["https://openalex.org/I191429286"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ken W. Smith","raw_affiliation_strings":["Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77341, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77341, U.S.A","institution_ids":["https://openalex.org/I191429286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010712874","display_name":"Brett Stevens","orcid":"https://orcid.org/0000-0003-4336-1773"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brett Stevens","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa ON K1S 5B6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa ON K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5038008468"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07279241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","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":0.992900013923645,"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":0.992900013923645,"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":0.9553999900817871,"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/T12504","display_name":"Mathematics and Applications","score":0.9174000024795532,"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/affine-transformation","display_name":"Affine transformation","score":0.6825272440910339},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.6443789601325989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5156965851783752},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.4791252613067627},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39412444829940796},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37215685844421387},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22827088832855225}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6825272440910339},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6443789601325989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5156965851783752},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.4791252613067627},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39412444829940796},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37215685844421387},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22827088832855225},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c64163845","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64163845","pdf_url":"https://escholarship.org/content/qt6q20z7sg/qt6q20z7sg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt6q20z7sg","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/6q20z7sg","pdf_url":"https://escholarship.org/content/qt6q20z7sg/qt6q20z7sg.pdf?t=sfxprg","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"Combinatorial Theory, vol 4, iss 1","raw_type":"article"}],"best_oa_location":{"id":"doi:10.5070/c64163845","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64163845","pdf_url":"https://escholarship.org/content/qt6q20z7sg/qt6q20z7sg.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400196885.pdf","grobid_xml":"https://content.openalex.org/works/W4400196885.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1965510685","https://openalex.org/W1990948848","https://openalex.org/W2025047923","https://openalex.org/W2043260611","https://openalex.org/W2046272424","https://openalex.org/W2052060691","https://openalex.org/W2061504572","https://openalex.org/W2073367256","https://openalex.org/W2092909034","https://openalex.org/W2093978752","https://openalex.org/W2124113125","https://openalex.org/W2148580005","https://openalex.org/W2286055821","https://openalex.org/W2518939738","https://openalex.org/W2577848484","https://openalex.org/W2619826047","https://openalex.org/W2794160495","https://openalex.org/W3012386464","https://openalex.org/W4205545339","https://openalex.org/W4234238940","https://openalex.org/W4299482635"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2001489718","https://openalex.org/W2024319036","https://openalex.org/W1549557214","https://openalex.org/W1982071305","https://openalex.org/W2026311931","https://openalex.org/W2004502427","https://openalex.org/W2073468254","https://openalex.org/W2038968071","https://openalex.org/W3099986201"],"abstract_inverted_index":{"A":[0],"pair":[1],"of":[2,9,24,30,48,65,79],"planes,":[3,51,95,97],"both":[4,7,52],"projective":[5,53,94],"or":[6],"affine,":[8,55],"the":[10,15,31,75],"same":[11,16],"order":[12],"and":[13,54,56,83],"on":[14],"point":[17],"set":[18],"are":[19,61],"orthogoval":[20,50,70,81,100],"if":[21],"each":[22,28],"line":[23,29],"one":[25],"plane":[26,33],"intersects":[27],"other":[32],"in":[34],"at":[35],"most":[36],"two":[37,68],"points.":[38],"In":[39],"this":[40],"paper":[41],"we":[42],"prove":[43],"new":[44],"constructions":[45],"for":[46],"sets":[47,64,78],"mutually":[49,69,80],"review":[57],"known":[58],"results":[59],"that":[60],"equivalent":[62],"to":[63],"more":[66],"than":[67],"planes.":[71],"We":[72],"also":[73],"discuss":[74],"connection":[76],"between":[77],"planes":[82,101],"covering":[84,98],"arrays.Mathematics":[85],"Subject":[86],"Classifications:":[87],"05B25,":[88],"05B40,":[89],"51E20,":[90],"51E21Keywords:":[91],"Finite":[92],"geometry,":[93],"affine":[96],"arrays,":[99]},"counts_by_year":[],"updated_date":"2026-03-07T13:37:22.277990","created_date":"2025-10-10T00:00:00"}
