{"id":"https://openalex.org/W2047485915","doi":"https://doi.org/10.1134/s0032946014040036","title":"Upper bounds on the smallest size of a complete arc in PG(2, q) under a certain probabilistic conjecture","display_name":"Upper bounds on the smallest size of a complete arc in PG(2, q) under a certain probabilistic conjecture","publication_year":2014,"publication_date":"2014-10-01","ids":{"openalex":"https://openalex.org/W2047485915","doi":"https://doi.org/10.1134/s0032946014040036","mag":"2047485915"},"language":"en","primary_location":{"id":"doi:10.1134/s0032946014040036","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946014040036","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075822892","display_name":"Daniele Bartoli","orcid":"https://orcid.org/0000-0002-5767-1679"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["IT","RU"],"is_corresponding":true,"raw_author_name":"D. Bartoli","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]},{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018158772","display_name":"Alexander A. Davydov","orcid":"https://orcid.org/0000-0002-5827-4560"},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. A. Davydov","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088731018","display_name":"Giorgio Faina","orcid":"https://orcid.org/0000-0002-0230-7976"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Faina","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063343785","display_name":"Alexey Kreshchuk","orcid":"https://orcid.org/0000-0001-6574-5538"},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. A. Kreshchuk","raw_affiliation_strings":["Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028598034","display_name":"Stefano Marcugini","orcid":"https://orcid.org/0000-0002-7961-0260"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Marcugini","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010058458","display_name":"Fernanda Pambianco","orcid":"https://orcid.org/0000-0001-5476-5365"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. Pambianco","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5075822892"],"corresponding_institution_ids":["https://openalex.org/I27483092","https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":2.1887,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85461516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"50","issue":"4","first_page":"320","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","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/T10849","display_name":"Finite Group Theory Research","score":0.9952999949455261,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8103688359260559},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7825567126274109},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7298055291175842},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.5823882818222046},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5333673357963562},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.49804186820983887},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4805503487586975},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.41143599152565},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.365642249584198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1728384792804718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11256533861160278}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8103688359260559},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7825567126274109},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7298055291175842},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5823882818222046},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5333673357963562},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.49804186820983887},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4805503487586975},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.41143599152565},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.365642249584198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1728384792804718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11256533861160278},{"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:10.1134/s0032946014040036","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946014040036","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W59572088","https://openalex.org/W63585748","https://openalex.org/W177027056","https://openalex.org/W648165475","https://openalex.org/W1429261892","https://openalex.org/W1536740749","https://openalex.org/W1543072686","https://openalex.org/W1565617150","https://openalex.org/W1896299118","https://openalex.org/W1967457258","https://openalex.org/W1971795835","https://openalex.org/W1972100851","https://openalex.org/W1979782690","https://openalex.org/W1985188998","https://openalex.org/W1986731159","https://openalex.org/W1986960688","https://openalex.org/W1992397673","https://openalex.org/W1994461021","https://openalex.org/W1995747335","https://openalex.org/W2001746495","https://openalex.org/W2003543155","https://openalex.org/W2010411207","https://openalex.org/W2012312289","https://openalex.org/W2013412009","https://openalex.org/W2014025706","https://openalex.org/W2023820155","https://openalex.org/W2025746263","https://openalex.org/W2030279030","https://openalex.org/W2031781956","https://openalex.org/W2036974936","https://openalex.org/W2037488180","https://openalex.org/W2039270103","https://openalex.org/W2043057332","https://openalex.org/W2053395706","https://openalex.org/W2057900706","https://openalex.org/W2061614044","https://openalex.org/W2061838236","https://openalex.org/W2065628830","https://openalex.org/W2068948350","https://openalex.org/W2074069969","https://openalex.org/W2074097394","https://openalex.org/W2094071977","https://openalex.org/W2106405826","https://openalex.org/W2112765613","https://openalex.org/W2113827468","https://openalex.org/W2124113125","https://openalex.org/W2146259740","https://openalex.org/W2158815455","https://openalex.org/W2159759788","https://openalex.org/W2163244493","https://openalex.org/W2165509710","https://openalex.org/W2327911790","https://openalex.org/W2335532532","https://openalex.org/W2340949728","https://openalex.org/W2473381345","https://openalex.org/W2583739487","https://openalex.org/W2593295532","https://openalex.org/W2751862591","https://openalex.org/W2801298029","https://openalex.org/W2914323373","https://openalex.org/W2962759307","https://openalex.org/W4210284285","https://openalex.org/W4236333147","https://openalex.org/W4251087198","https://openalex.org/W4299432846"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W2544839741","https://openalex.org/W4300899577","https://openalex.org/W3194471551","https://openalex.org/W184455116","https://openalex.org/W4375956809","https://openalex.org/W2058473748","https://openalex.org/W3006266956"],"abstract_inverted_index":{"In":[0],"the":[1,32,41,49,66,70,82,149,158,170,174,191,195],"projective":[2],"plane":[3],"PG(2,":[4,93],"q),":[5,94],"we":[6,44,77],"consider":[7],"an":[8,46],"iterative":[9,42],"construction":[10],"of":[11,38,40,51,88,132,142,148,162,169,184,190],"complete":[12,90,163],"arcs":[13,164],"which":[14],"adds":[15],"a":[16,75,89,181,188],"new":[17,150],"point":[18],"in":[19,55,92,95,166,173,180],"each":[20],"step.":[21,57],"It":[22],"is":[23,63,152],"proved":[24],"that":[25,65],"uncovered":[26],"points":[27,54],"are":[28,139],"uniformly":[29],"distributed":[30],"over":[31],"plane.":[33],"For":[34],"more":[35],"than":[36],"half":[37],"steps":[39,72],"process,":[43],"prove":[45],"estimate":[47,67],"for":[48,69],"number":[50],"newly":[52],"covered":[53],"every":[56],"A":[58],"natural":[59],"(and":[60],"well-founded)":[61],"conjecture":[62],"made":[64],"holds":[68],"other":[71],"too.":[73],"As":[74],"result,":[76],"obtain":[78],"upper":[79,133],"bounds":[80,134,151],"on":[81,135],"smallest":[83,159],"size":[84],"t":[85,136],"2(2,":[86,137],"q)":[87,138],"arc":[91],"particular,":[96],"$$\\begin{array}{*{20}c}":[97],"{t_2":[98,121],"(2,q)":[99,122],"<":[100,123],"\\sqrt":[101,103,114],"q":[102,105,109],"{3\\ln":[104],"+":[106,110,113,118],"\\ln":[107,108,111],"3}":[112],"{\\frac{q}":[115],"{{3\\ln":[116],"q}}}":[117],"3,}":[119],"\\\\":[120,128],"1.87\\sqrt":[124],"{q\\ln":[125],"q}":[126],".}":[127],"\\end{array}$$":[129],"Nonstandard":[130],"types":[131],"considered,":[140],"one":[141],"them":[143,156],"being":[144],"new.":[145],"The":[146],"effectiveness":[147],"illustrated":[153],"by":[154],"comparing":[155],"with":[157,194],"known":[160],"sizes":[161],"obtained":[165],"recent":[167],"works":[168],"authors":[171],"and":[172],"present":[175],"paper":[176],"via":[177],"computer":[178],"search":[179],"wide":[182],"region":[183],"q.":[185],"We":[186],"note":[187],"connection":[189],"considered":[192],"problems":[193],"so-called":[196],"birthday":[197,200],"problem":[198],"(or":[199],"paradox).":[201]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}