{"id":"https://openalex.org/W3159201129","doi":"https://doi.org/10.1007/s10623-022-01033-3","title":"On $$\\alpha $$-points of q-analogs of the Fano plane","display_name":"On $$\\alpha $$-points of q-analogs of the Fano plane","publication_year":2022,"publication_date":"2022-04-27","ids":{"openalex":"https://openalex.org/W3159201129","doi":"https://doi.org/10.1007/s10623-022-01033-3","mag":"3159201129"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-022-01033-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01033-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01033-3.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01033-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Michael Kiermaier","orcid":"https://orcid.org/0000-0002-5901-4381"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Kiermaier","raw_affiliation_strings":["Universit\u00e4t Bayreuth, Mathematisches Institut, 95440, Bayreuth, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Bayreuth, Mathematisches Institut, 95440, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00383902,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"90","issue":"6","first_page":"1335","last_page":"1345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9988999962806702,"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":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.7128322720527649},{"id":"https://openalex.org/keywords/fano-plane","display_name":"Fano plane","score":0.5565786957740784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.502295732498169},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39103618264198303},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37542152404785156},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36797598004341125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2801259160041809},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19731271266937256}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7128322720527649},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.5565786957740784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.502295732498169},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39103618264198303},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37542152404785156},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36797598004341125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2801259160041809},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19731271266937256}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10623-022-01033-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01033-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01033-3.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:epub.uni-bayreuth.de:6621","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:arXiv.org:2105.00365","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2105.00365","pdf_url":"https://arxiv.org/pdf/2105.00365","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eref.uni-bayreuth.de:71787","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/71787/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":{"id":"doi:10.1007/s10623-022-01033-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-022-01033-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-022-01033-3.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322634","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3159201129.pdf","grobid_xml":"https://content.openalex.org/works/W3159201129.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1566931862","https://openalex.org/W1583183878","https://openalex.org/W1876525288","https://openalex.org/W1949087419","https://openalex.org/W1977209878","https://openalex.org/W1985627461","https://openalex.org/W1991497121","https://openalex.org/W1996268096","https://openalex.org/W1999534475","https://openalex.org/W2006742849","https://openalex.org/W2021537862","https://openalex.org/W2033975155","https://openalex.org/W2049020435","https://openalex.org/W2050354656","https://openalex.org/W2057190613","https://openalex.org/W2080353482","https://openalex.org/W2086724086","https://openalex.org/W2245663796","https://openalex.org/W2387239251","https://openalex.org/W2512896814","https://openalex.org/W2555021951","https://openalex.org/W2574078915","https://openalex.org/W2791754941","https://openalex.org/W2963286138","https://openalex.org/W2963529046","https://openalex.org/W2963767774","https://openalex.org/W3098523922","https://openalex.org/W3103815971","https://openalex.org/W3122418194","https://openalex.org/W4231387828","https://openalex.org/W4288997455"],"related_works":["https://openalex.org/W2886806333","https://openalex.org/W2954712024","https://openalex.org/W1974030747","https://openalex.org/W3151815251","https://openalex.org/W4300636821","https://openalex.org/W2067732528","https://openalex.org/W2952621279","https://openalex.org/W2964222469","https://openalex.org/W1641727897","https://openalex.org/W4327909833"],"abstract_inverted_index":{"Abstract":[0],"Arguably,":[1],"the":[2,8,16,19,27,44,63,94,123,140,161,167,180],"most":[3],"important":[4],"open":[5],"problem":[6],"in":[7,68,118],"theory":[9],"of":[10,13,21,26,31,43,60,66,152,163,166,182,196],"q":[11,23,42,173,191,197],"-analogs":[12],"designs":[14],"is":[15,50,70,186],"question":[17],"regarding":[18],"existence":[20,162],"a":[22,71,84,134,148,164,178],"-analog":[24],"D":[25,61,67],"Fano":[28],"plane.":[29],"As":[30,177],"today,":[32],"it":[33],"remains":[34],"undecided":[35],"for":[36],"every":[37],"single":[38],"prime":[39],"power":[40],"order":[41],"base":[45],"field.":[46],"A":[47],"point":[48],"P":[49,69],"called":[51],"an":[52],"$$\\alpha":[53,86,125,153],"$$":[54,87,126,154],"<mml:math":[55,88,100,127,155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[56,89,101,128,156],"<mml:mi>\u03b1</mml:mi>":[57,90,129,157],"</mml:math>":[58,91,107,130,158],"-point":[59],"if":[62],"derived":[64],"design":[65],"geometric":[72],"spread.":[73],"In":[74,142],"1996,":[75],"Simon":[76],"Thomas":[77],"has":[78],"shown":[79],"that":[80,122,147],"there":[81],"always":[82],"exists":[83],"non-":[85,124],"-point.":[92],"For":[93],"binary":[95],"case":[96],"$$q":[97],"=":[98],"2$$":[99],"<mml:mrow>":[102],"<mml:mi>q</mml:mi>":[103],"<mml:mo>=</mml:mo>":[104],"<mml:mn>2</mml:mn>":[105],"</mml:mrow>":[106],",":[108],"Olof":[109],"Heden":[110,183],"and":[111,184,192],"Papa":[112],"Sissokho":[113,185],"have":[114],"improved":[115],"this":[116,143],"result":[117],"2016":[119],"by":[120],"showing":[121],"-points":[131,159],"must":[132],"form":[133],"blocking":[135],"set":[136],"with":[137],"respect":[138],"to":[139,188],"hyperplanes.":[141],"article,":[144],"we":[145],"show":[146],"hyperplane":[149],"consisting":[150],"only":[151],"implies":[160],"partition":[165],"symplectic":[168],"generalized":[169,187],"quadrangle":[170],"W":[171],"(":[172],")":[174],"into":[175],"spreads.":[176],"consequence,":[179],"statement":[181],"all":[189,193],"primes":[190],"even":[194],"values":[195],".":[198]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2021-05-10T00:00:00"}
